LMFDB - Embedded newform 15.4.e.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,4,Mod(2,15)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.885028650086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$-2.66260 + 2.66260i$ of defining polynomial
Character	$\chi$	$=$	15.8
Dual form			15.4.e.a.2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +O(q^{10})$	\(q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +(-40.8945 - 10.0000i) q^{10} -34.1375i q^{11} +(17.3301 - 27.0278i) q^{12} +(2.82109 + 2.82109i) q^{13} -49.8323 q^{14} +(-58.0772 - 1.42827i) q^{15} +75.2524 q^{16} +(64.2384 + 64.2384i) q^{17} +(35.3316 - 95.3316i) q^{18} +19.0735i q^{19} +(35.8474 + 59.0536i) q^{20} +(-67.1789 + 14.6869i) q^{21} +(-90.8945 + 90.8945i) q^{22} +(-51.4018 + 51.4018i) q^{23} +(34.8094 - 7.61018i) q^{24} +(57.6836 - 110.895i) q^{25} -15.0229i q^{26} +(19.5337 - 138.930i) q^{27} +(57.8211 + 57.8211i) q^{28} +50.5042 q^{29} +(150.834 + 158.439i) q^{30} -93.3673 q^{31} +(-161.576 - 161.576i) q^{32} +(-95.7458 + 149.324i) q^{33} -342.083i q^{34} +(35.1454 - 143.725i) q^{35} +(-151.610 + 69.6188i) q^{36} +(-161.537 + 161.537i) q^{37} +(50.7850 - 50.7850i) q^{38} +(-4.42765 - 20.2524i) q^{39} +(-18.2109 + 74.4727i) q^{40} +88.7935i q^{41} +(217.976 + 139.765i) q^{42} +(176.399 + 176.399i) q^{43} +210.932 q^{44} +(250.035 + 169.137i) q^{45} +273.725 q^{46} +(38.2843 + 38.2843i) q^{47} +(-329.169 - 211.061i) q^{48} +167.863i q^{49} +(-448.857 + 141.680i) q^{50} +(-100.821 - 461.162i) q^{51} +(-17.4313 + 17.4313i) q^{52} +(344.569 - 344.569i) q^{53} +(-421.925 + 317.904i) q^{54} +(-198.051 - 326.262i) q^{55} +90.7492i q^{56} +(53.4956 - 83.4310i) q^{57} +(-134.473 - 134.473i) q^{58} -421.133 q^{59} +(8.82514 - 358.854i) q^{60} +2.00000 q^{61} +(248.600 + 248.600i) q^{62} +(335.046 + 124.174i) q^{63} +258.409i q^{64} +(43.3287 + 10.5952i) q^{65} +(652.524 - 142.657i) q^{66} +(430.987 - 430.987i) q^{67} +(-396.923 + 396.923i) q^{68} +(369.009 - 80.6742i) q^{69} +(-476.262 + 289.105i) q^{70} +733.866i q^{71} +(-173.607 - 64.3420i) q^{72} +(-348.073 - 348.073i) q^{73} +860.216 q^{74} +(-563.347 + 323.288i) q^{75} -117.853 q^{76} +(-319.452 - 319.452i) q^{77} +(-42.1349 + 65.7131i) q^{78} +588.019i q^{79} +(719.209 - 436.582i) q^{80} +(-475.102 + 552.919i) q^{81} +(236.422 - 236.422i) q^{82} +(-217.997 + 217.997i) q^{83} +(-90.7492 - 415.092i) q^{84} +(986.629 + 241.262i) q^{85} -939.362i q^{86} +(-220.915 - 141.650i) q^{87} +(165.527 + 165.527i) q^{88} -1272.00 q^{89} +(-215.399 - 1116.09i) q^{90} +52.7985 q^{91} +(-317.607 - 317.607i) q^{92} +(408.407 + 261.868i) q^{93} -203.872i q^{94} +(110.656 + 182.291i) q^{95} +(253.591 + 1159.94i) q^{96} +(-432.111 + 432.111i) q^{97} +(446.951 - 446.951i) q^{98} +(837.622 - 384.633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.66260	−	2.66260i	−0.941372	−	0.941372i	0.0570018	−	0.998374i	$-0.481846\pi$
$2$	−2.66260	−	2.66260i	−0.941372	−	0.941372i	−0.998374	+	0.0570018i	$0.981846\pi$
$3$	−4.37420	−	2.80471i	−0.841814	−	0.539767i
$3$	−4.37420	−	2.80471i	−0.841814	−	0.539767i
$4$			6.17891i			0.772364i
$5$	9.55729	−	5.80157i	0.854830	−	0.518908i
$5$	9.55729	−	5.80157i	0.854830	−	0.518908i
$6$	4.17891	+	19.1146i	0.284339	+	1.30058i
$7$	9.35782	−	9.35782i	0.505275	−	0.505275i	−0.407798	−	0.913072i	$-0.633703\pi$
$7$	9.35782	−	9.35782i	0.505275	−	0.505275i	0.913072	+	0.407798i	$0.133703\pi$
$8$	−4.84884	+	4.84884i	−0.214291	+	0.214291i
$9$	11.2672	+	24.5367i	0.417303	+	0.908768i
$10$	−40.8945	−	10.0000i	−1.29320	−	0.316228i
$11$		−	34.1375i		−	0.935712i	−0.883805	−	0.467856i	$-0.845027\pi$
$11$		−	34.1375i		−	0.935712i	0.883805	−	0.467856i	$-0.154973\pi$
$12$	17.3301	−	27.0278i	0.416897	−	0.650187i
$13$	2.82109	+	2.82109i	0.0601869	+	0.0601869i	0.736560	−	0.676373i	$-0.236449\pi$
$13$	2.82109	+	2.82109i	0.0601869	+	0.0601869i	−0.676373	+	0.736560i	$0.736449\pi$
$14$	−49.8323			−0.951303
$15$	−58.0772	−	1.42827i	−0.999698	−	0.0245851i
$16$	75.2524			1.17582
$17$	64.2384	+	64.2384i	0.916477	+	0.916477i	0.996771	−	0.0802942i	$-0.0255860\pi$
$17$	64.2384	+	64.2384i	0.916477	+	0.916477i	−0.0802942	+	0.996771i	$0.525586\pi$
$18$	35.3316	−	95.3316i	0.462652	−	1.24833i
$19$			19.0735i			0.230303i	0.993348	+	0.115151i	$0.0367353\pi$
$19$			19.0735i			0.230303i	−0.993348	+	0.115151i	$0.963265\pi$
$20$	35.8474	+	59.0536i	0.400786	+	0.660240i
$21$	−67.1789	+	14.6869i	−0.698078	+	0.152617i
$22$	−90.8945	+	90.8945i	−0.880854	+	0.880854i
$23$	−51.4018	+	51.4018i	−0.466001	+	0.466001i	−0.900616	−	0.434616i	$-0.856884\pi$
$23$	−51.4018	+	51.4018i	−0.466001	+	0.466001i	0.434616	+	0.900616i	$0.356884\pi$
$24$	34.8094	−	7.61018i	0.296060	−	0.0647259i
$25$	57.6836	−	110.895i	0.461469	−	0.887156i
$26$		−	15.0229i		−	0.113317i
$27$	19.5337	−	138.930i	0.139232	−	0.990260i
$28$	57.8211	+	57.8211i	0.390256	+	0.390256i
$29$	50.5042			0.323393			0.161697	−	0.986841i	$-0.448303\pi$
$29$	50.5042			0.323393			0.161697	+	0.986841i	$0.448303\pi$
$30$	150.834	+	158.439i	0.917944	+	0.964232i
$31$	−93.3673			−0.540944			−0.270472	−	0.962728i	$-0.587180\pi$
$31$	−93.3673			−0.540944			−0.270472	+	0.962728i	$0.587180\pi$
$32$	−161.576	−	161.576i	−0.892592	−	0.892592i
$33$	−95.7458	+	149.324i	−0.505067	+	0.787696i
$34$		−	342.083i		−	1.72549i
$35$	35.1454	−	143.725i	0.169733	−	0.694115i
$36$	−151.610	+	69.6188i	−0.701899	+	0.322309i
$37$	−161.537	+	161.537i	−0.717743	+	0.717743i	−0.968142	−	0.250400i	$-0.919438\pi$
$37$	−161.537	+	161.537i	−0.717743	+	0.717743i	0.250400	+	0.968142i	$0.419438\pi$
$38$	50.7850	−	50.7850i	0.216800	−	0.216800i
$39$	−4.42765	−	20.2524i	−0.0181793	−	0.0831531i
$40$	−18.2109	+	74.4727i	−0.0719850	+	0.294379i
$41$			88.7935i			0.338225i	0.985597	+	0.169112i	$0.0540901\pi$
$41$			88.7935i			0.338225i	−0.985597	+	0.169112i	$0.945910\pi$
$42$	217.976	+	139.765i	0.800820	+	0.513482i
$43$	176.399	+	176.399i	0.625596	+	0.625596i	0.946957	−	0.321361i	$-0.104140\pi$
$43$	176.399	+	176.399i	0.625596	+	0.625596i	−0.321361	+	0.946957i	$0.604140\pi$
$44$	210.932			0.722710
$45$	250.035	+	169.137i	0.828290	+	0.560300i
$46$	273.725			0.877360
$47$	38.2843	+	38.2843i	0.118816	+	0.118816i	0.764015	−	0.645199i	$-0.223225\pi$
$47$	38.2843	+	38.2843i	0.118816	+	0.118816i	−0.645199	+	0.764015i	$0.723225\pi$
$48$	−329.169	−	211.061i	−0.989820	−	0.634668i
$49$			167.863i			0.489395i
$50$	−448.857	+	141.680i	−1.26956	+	0.400730i
$51$	−100.821	−	461.162i	−0.276819	−	1.26619i
$52$	−17.4313	+	17.4313i	−0.0464862	+	0.0464862i
$53$	344.569	−	344.569i	0.893022	−	0.893022i	−0.101784	−	0.994806i	$-0.532455\pi$
$53$	344.569	−	344.569i	0.893022	−	0.893022i	0.994806	+	0.101784i	$0.0324551\pi$
$54$	−421.925	+	317.904i	−1.06327	+	0.801134i
$55$	−198.051	−	326.262i	−0.485549	−	0.799875i
$56$			90.7492i			0.216551i
$57$	53.4956	−	83.4310i	0.124310	−	0.193872i
$58$	−134.473	−	134.473i	−0.304433	−	0.304433i
$59$	−421.133			−0.929268			−0.464634	−	0.885503i	$-0.653814\pi$
$59$	−421.133			−0.929268			−0.464634	+	0.885503i	$0.653814\pi$
$60$	8.82514	−	358.854i	0.0189887	−	0.772130i
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$	248.600	+	248.600i	0.509229	+	0.509229i
$63$	335.046	+	124.174i	0.670030	+	0.248325i
$64$			258.409i			0.504704i
$65$	43.3287	+	10.5952i	0.0826811	+	0.0202181i
$66$	652.524	−	142.657i	1.21697	−	0.266059i
$67$	430.987	−	430.987i	0.785872	−	0.785872i	−0.194943	−	0.980815i	$-0.562452\pi$
$67$	430.987	−	430.987i	0.785872	−	0.785872i	0.980815	+	0.194943i	$0.0624521\pi$
$68$	−396.923	+	396.923i	−0.707853	+	0.707853i
$69$	369.009	−	80.6742i	0.643818	−	0.140754i
$70$	−476.262	+	289.105i	−0.813202	+	0.493639i
$71$			733.866i			1.22667i	0.789822	+	0.613337i	$0.210173\pi$
$71$			733.866i			1.22667i	−0.789822	+	0.613337i	$0.789827\pi$
$72$	−173.607	−	64.3420i	−0.284164	−	0.105316i
$73$	−348.073	−	348.073i	−0.558067	−	0.558067i	0.370690	−	0.928757i	$-0.379121\pi$
$73$	−348.073	−	348.073i	−0.558067	−	0.558067i	−0.928757	+	0.370690i	$0.879121\pi$
$74$	860.216			1.35133
$75$	−563.347	+	323.288i	−0.867329	+	0.497735i
$76$	−117.853			−0.177877
$77$	−319.452	−	319.452i	−0.472792	−	0.472792i
$78$	−42.1349	+	65.7131i	−0.0611646	+	0.0953915i
$79$			588.019i			0.837434i	0.908117	+	0.418717i	$0.137520\pi$
$79$			588.019i			0.837434i	−0.908117	+	0.418717i	$0.862480\pi$
$80$	719.209	−	436.582i	1.00512	−	0.610141i
$81$	−475.102	+	552.919i	−0.651717	+	0.758462i
$82$	236.422	−	236.422i	0.318395	−	0.318395i
$83$	−217.997	+	217.997i	−0.288293	+	0.288293i	−0.836405	−	0.548112i	$-0.815347\pi$
$83$	−217.997	+	217.997i	−0.288293	+	0.288293i	0.548112	+	0.836405i	$0.315347\pi$
$84$	−90.7492	−	415.092i	−0.117876	−	0.539170i
$85$	986.629	+	241.262i	1.25900	+	0.307865i
$86$		−	939.362i		−	1.17784i
$87$	−220.915	−	141.650i	−0.272237	−	0.174557i
$88$	165.527	+	165.527i	0.200514	+	0.200514i
$89$	−1272.00			−1.51497			−0.757483	−	0.652855i	$-0.773571\pi$
$89$	−1272.00			−1.51497			−0.757483	+	0.652855i	$0.773571\pi$
$90$	−215.399	−	1116.09i	−0.252278	−	1.30718i
$91$	52.7985			0.0608219
$92$	−317.607	−	317.607i	−0.359922	−	0.359922i
$93$	408.407	+	261.868i	0.455374	+	0.291984i
$94$		−	203.872i		−	0.223700i
$95$	110.656	+	182.291i	0.119506	+	0.196870i
$96$	253.591	+	1159.94i	0.269605	+	1.23319i
$97$	−432.111	+	432.111i	−0.452312	+	0.452312i	−0.896121	−	0.443809i	$-0.853627\pi$
$97$	−432.111	+	432.111i	−0.452312	+	0.452312i	0.443809	+	0.896121i	$0.353627\pi$
$98$	446.951	−	446.951i	0.460703	−	0.460703i
$99$	837.622	−	384.633i	0.850345	−	0.390475i
$100$	685.207	+	356.422i	0.685207	+	0.356422i
$101$		−	1662.30i		−	1.63767i	−0.574029	−	0.818835i	$-0.694620\pi$
$101$		−	1662.30i		−	1.63767i	0.574029	−	0.818835i	$-0.305380\pi$
$102$	−959.444	+	1496.34i	−0.931364	+	1.45254i
$103$	−774.495	−	774.495i	−0.740906	−	0.740906i	0.231847	−	0.972752i	$-0.425523\pi$
$103$	−774.495	−	774.495i	−0.740906	−	0.740906i	−0.972752	+	0.231847i	$0.925523\pi$
$104$	−27.3581			−0.0257950
$105$	−556.841	+	530.110i	−0.517544	+	0.492700i
$106$	−1834.90			−1.68133
$107$	1170.26	+	1170.26i	1.05732	+	1.05732i	0.998254	+	0.0590633i	$0.0188114\pi$
$107$	1170.26	+	1170.26i	1.05732	+	1.05732i	0.0590633	+	0.998254i	$0.481189\pi$
$108$	858.433	+	120.697i	0.764841	+	0.107537i
$109$		−	1264.60i		−	1.11125i	−0.831432	−	0.555627i	$-0.812478\pi$
$109$		−	1264.60i		−	1.11125i	0.831432	−	0.555627i	$-0.187522\pi$
$110$	−341.375	+	1396.04i	−0.295898	+	1.21006i
$111$	1159.66	−	253.529i	0.991620	−	0.216792i
$112$	704.198	−	704.198i	0.594111	−	0.594111i
$113$	−381.173	+	381.173i	−0.317325	+	0.317325i	−0.847739	−	0.530414i	$-0.822037\pi$
$113$	−381.173	+	381.173i	−0.317325	+	0.317325i	0.530414	+	0.847739i	$0.322037\pi$
$114$	−364.581	+	79.7062i	−0.299528	+	0.0654839i
$115$	−193.051	+	789.473i	−0.156540	+	0.640163i
$116$			312.061i			0.249777i
$117$	−37.4346	+	101.006i	−0.0295798	+	0.0798121i
$118$	1121.31	+	1121.31i	0.874787	+	0.874787i
$119$	1202.26			0.926145
$120$	288.533	−	274.682i	0.219494	−	0.208958i
$121$	165.633			0.124442
$122$	−5.32521	−	5.32521i	−0.00395182	−	0.00395182i
$123$	249.040	−	388.400i	0.182563	−	0.284722i
$124$		−	576.908i		−	0.417805i
$125$	−92.0630	−	1394.51i	−0.0658749	−	0.997828i
$126$	−561.469	−	1222.72i	−0.396981	−	0.864513i
$127$	−439.588	+	439.588i	−0.307142	+	0.307142i	−0.843800	−	0.536658i	$-0.819687\pi$
$127$	−439.588	+	439.588i	−0.307142	+	0.307142i	0.536658	+	0.843800i	$0.319687\pi$
$128$	−604.571	+	604.571i	−0.417477	+	0.417477i
$129$	−276.856	−	1266.35i	−0.188959	−	0.864312i
$130$	−87.1563	−	143.578i	−0.0588009	−	0.0968664i
$131$			1399.28i			0.933247i	0.884456	+	0.466623i	$0.154530\pi$
$131$			1399.28i			0.933247i	−0.884456	+	0.466623i	$0.845470\pi$
$132$	−922.659	−	591.605i	−0.608388	−	0.390095i
$133$	178.486	+	178.486i	0.116366	+	0.116366i
$134$	−2295.09			−1.47960
$135$	−619.321	−	1441.12i	−0.394834	−	0.918752i
$136$	−622.964			−0.392785
$137$	−1092.28	−	1092.28i	−0.681169	−	0.681169i	0.279095	−	0.960264i	$-0.409966\pi$
$137$	−1092.28	−	1092.28i	−0.681169	−	0.681169i	−0.960264	+	0.279095i	$0.909966\pi$
$138$	−1197.33	−	767.720i	−0.738574	−	0.473570i
$139$			2498.43i			1.52456i	0.647245	+	0.762282i	$0.275921\pi$
$139$			2498.43i			1.52456i	−0.647245	+	0.762282i	$0.724079\pi$
$140$	888.066	+	217.160i	0.536109	+	0.131096i
$141$	−60.0866	−	274.840i	−0.0358880	−	0.164154i
$142$	1953.99	−	1953.99i	1.15476	−	1.15476i
$143$	96.3049	−	96.3049i	0.0563177	−	0.0563177i
$144$	847.881	+	1846.45i	0.490672	+	1.06855i
$145$	482.684	−	293.004i	0.276446	−	0.167811i
$146$			1853.56i			1.05070i
$147$	470.806	−	734.264i	0.264159	−	0.411980i
$148$	−998.121	−	998.121i	−0.554358	−	0.554358i
$149$	3570.40			1.96308			0.981538	−	0.191270i	$-0.0612605\pi$
$149$	3570.40			1.96308			0.981538	+	0.191270i	$0.0612605\pi$
$150$	2360.76	+	639.180i	1.28503	+	0.347926i
$151$	2687.14			1.44819			0.724094	−	0.689701i	$-0.242258\pi$
$151$	2687.14			1.44819			0.724094	+	0.689701i	$0.242258\pi$
$152$	−92.4842	−	92.4842i	−0.0493517	−	0.0493517i
$153$	−852.415	+	2299.99i	−0.450416	+	1.21531i
$154$			1701.15i			0.890146i
$155$	−892.338	+	541.676i	−0.462415	+	0.280700i
$156$	125.137	−	27.3581i	0.0642245	−	0.0140410i
$157$	−1810.48	+	1810.48i	−0.920333	+	0.920333i	−0.997053	−	0.0767201i	$-0.975555\pi$
$157$	−1810.48	+	1810.48i	−0.920333	+	0.920333i	0.0767201	+	0.997053i	$0.475555\pi$
$158$	1565.66	−	1565.66i	0.788337	−	0.788337i
$159$	−2473.63	+	540.795i	−1.23378	+	0.269735i
$160$	−2481.63	−	606.836i	−1.22619	−	0.299841i
$161$			962.017i			0.470916i
$162$	2737.21	−	207.196i	1.32750	−	0.100487i
$163$	−2679.06	−	2679.06i	−1.28736	−	1.28736i	−0.936382	−	0.350982i	$-0.885848\pi$
$163$	−2679.06	−	2679.06i	−1.28736	−	1.28736i	−0.350982	−	0.936382i	$-0.614152\pi$
$164$	−548.647			−0.261232
$165$	−48.7575	+	1982.61i	−0.0230046	+	0.935430i
$166$	1160.88			0.542782
$167$	−139.543	−	139.543i	−0.0646597	−	0.0646597i	0.674037	−	0.738697i	$-0.264559\pi$
$167$	−139.543	−	139.543i	−0.0646597	−	0.0646597i	−0.738697	+	0.674037i	$0.764559\pi$
$168$	254.525	−	396.955i	0.116887	−	0.182296i
$169$		−	2181.08i		−	0.992755i
$170$	−1984.62	−	3269.39i	−0.895372	−	1.47500i
$171$	−468.000	+	214.904i	−0.209292	+	0.0961059i
$172$	−1089.95	+	1089.95i	−0.483188	+	0.483188i
$173$	881.613	−	881.613i	0.387444	−	0.387444i	−0.486331	−	0.873775i	$-0.661665\pi$
$173$	881.613	−	881.613i	0.387444	−	0.387444i	0.873775	+	0.486331i	$0.161665\pi$
$174$	211.053	+	965.367i	0.0919532	+	0.420599i
$175$	−497.938	−	1577.52i	−0.215089	−	0.681426i
$176$		−	2568.93i		−	1.10023i
$177$	1842.12	+	1181.16i	0.782271	+	0.501588i
$178$	3386.84	+	3386.84i	1.42615	+	1.42615i
$179$	−2512.87			−1.04928			−0.524638	−	0.851325i	$-0.675799\pi$
$179$	−2512.87			−1.04928			−0.524638	+	0.851325i	$0.675799\pi$
$180$	−1045.08	+	1544.94i	−0.432755	+	0.639741i
$181$	269.796			0.110795			0.0553973	−	0.998464i	$-0.482357\pi$
$181$	269.796			0.110795			0.0553973	+	0.998464i	$0.482357\pi$
$182$	−140.581	−	140.581i	−0.0572560	−	0.0572560i
$183$	−8.74839	−	5.60943i	−0.00353388	−	0.00226591i
$184$		−	498.478i		−	0.199719i
$185$	−606.687	+	2481.02i	−0.241106	+	0.985990i
$186$	−390.173	−	1784.68i	−0.153811	−	0.703542i
$187$	2192.94	−	2192.94i	0.857559	−	0.857559i
$188$	−236.555	+	236.555i	−0.0917690	+	0.0917690i
$189$	−1117.29	−	1482.87i	−0.430003	−	0.570703i
$190$	190.735	−	780.000i	0.0728281	−	0.297827i
$191$		−	2420.22i		−	0.916864i	−0.888729	−	0.458432i	$-0.848411\pi$
$191$		−	2420.22i		−	0.916864i	0.888729	−	0.458432i	$-0.151589\pi$
$192$	724.762	−	1130.33i	0.272423	−	0.424867i
$193$	1965.28	+	1965.28i	0.732973	+	0.732973i	0.971208	−	0.238234i	$-0.0765686\pi$
$193$	1965.28	+	1965.28i	0.732973	+	0.732973i	−0.238234	+	0.971208i	$0.576569\pi$
$194$	2301.08			0.851588
$195$	−159.812	−	167.870i	−0.0586890	−	0.0616484i
$196$	−1037.21			−0.377991
$197$	832.602	+	832.602i	0.301119	+	0.301119i	0.841452	−	0.540333i	$-0.181702\pi$
$197$	832.602	+	832.602i	0.301119	+	0.301119i	−0.540333	+	0.841452i	$0.681702\pi$
$198$	−3254.38	−	1206.13i	−1.16807	−	0.432909i
$199$			1540.54i			0.548775i	0.961619	+	0.274387i	$0.0884750\pi$
$199$			1540.54i			0.548775i	−0.961619	+	0.274387i	$0.911525\pi$
$200$	258.011	+	817.409i	0.0912208	+	0.288998i
$201$	−3094.02	+	676.426i	−1.08575	+	0.237370i
$202$	−4426.04	+	4426.04i	−1.54166	+	1.54166i
$203$	472.609	−	472.609i	0.163402	−	0.163402i
$204$	2849.48	−	622.964i	0.977957	−	0.213805i
$205$	515.142	+	848.625i	0.175508	+	0.289125i
$206$			4124.35i			1.39494i
$207$	−1840.38	−	682.079i	−0.617949	−	0.229023i
$208$	212.294	+	212.294i	0.0707689	+	0.0707689i
$209$	651.119			0.215497
$210$	2894.12	+	71.1739i	0.951015	+	0.0233879i
$211$	−10.9380			−0.00356874			−0.00178437	−	0.999998i	$-0.500568\pi$
$211$	−10.9380			−0.00356874			−0.00178437	+	0.999998i	$0.500568\pi$
$212$	2129.06	+	2129.06i	0.689738	+	0.689738i
$213$	2058.28	−	3210.07i	0.662118	−	1.03263i
$214$		−	6231.86i		−	1.99066i
$215$	2709.29	+	662.507i	0.859405	+	0.210152i
$216$	578.932	+	768.364i	0.182367	+	0.242039i
$217$	−873.714	+	873.714i	−0.273325	+	0.273325i
$218$	−3367.13	+	3367.13i	−1.04610	+	1.04610i
$219$	546.295	+	2498.79i	0.168563	+	0.771016i
$220$	2015.94	−	1223.74i	0.617794	−	0.375020i
$221$			362.445i			0.110320i
$222$	−3762.75	−	2412.66i	−1.13757	−	0.729401i
$223$	831.512	+	831.512i	0.249696	+	0.249696i	0.820846	−	0.571150i	$-0.193503\pi$
$223$	831.512	+	831.512i	0.249696	+	0.249696i	−0.571150	+	0.820846i	$0.693503\pi$
$224$	−3024.00			−0.902008
$225$	3370.92	+	165.900i	0.998791	+	0.0491554i
$226$	2029.83			0.597443
$227$	−3441.18	−	3441.18i	−1.00616	−	1.00616i	−0.999981	−	0.00618314i	$-0.998032\pi$
$227$	−3441.18	−	3441.18i	−1.00616	−	1.00616i	−0.00618314	−	0.999981i	$-0.501968\pi$
$228$	515.512	+	330.544i	0.149740	+	0.0960124i
$229$		−	1680.38i		−	0.484903i	−0.970164	−	0.242451i	$-0.922049\pi$
$229$		−	1680.38i		−	0.484903i	0.970164	−	0.242451i	$-0.0779515\pi$
$230$	2616.07	−	1588.03i	0.749994	−	0.455269i
$231$	501.375	+	2293.32i	0.142805	+	0.653200i
$232$	−244.887	+	244.887i	−0.0693001	+	0.0693001i
$233$	−2106.74	+	2106.74i	−0.592348	+	0.592348i	−0.938265	−	0.345917i	$-0.887568\pi$
$233$	−2106.74	+	2106.74i	−0.592348	+	0.592348i	0.345917	+	0.938265i	$0.387568\pi$
$234$	368.613	−	169.265i	0.102978	−	0.0472873i
$235$	588.004	+	143.785i	0.163222	+	0.0399129i
$236$		−	2602.14i		−	0.717733i
$237$	1649.22	−	2572.11i	0.452019	−	0.704964i
$238$	−3201.15	−	3201.15i	−0.871847	−	0.871847i
$239$	261.125			0.0706728			0.0353364	−	0.999375i	$-0.488750\pi$
$239$	261.125			0.0706728			0.0353364	+	0.999375i	$0.488750\pi$
$240$	−4370.45	−	107.481i	−1.17546	−	0.0289077i
$241$	−6001.45			−1.60410			−0.802048	−	0.597259i	$-0.796256\pi$
$241$	−6001.45			−1.60410			−0.802048	+	0.597259i	$0.796256\pi$
$242$	−441.014	−	441.014i	−0.117147	−	0.117147i
$243$	3628.97	−	1086.05i	0.958018	−	0.286709i
$244$			12.3578i			0.00324233i
$245$	973.866	+	1604.31i	0.253951	+	0.418350i
$246$	−1697.25	+	371.060i	−0.439889	+	0.0961704i
$247$	−53.8080	+	53.8080i	−0.0138612	+	0.0138612i
$248$	452.723	−	452.723i	0.115919	−	0.115919i
$249$	1564.98	−	342.143i	0.398300	−	0.0870781i
$250$	−3467.89	+	3958.15i	−0.877315	+	1.00134i
$251$		−	3044.59i		−	0.765630i	−0.923825	−	0.382815i	$-0.874955\pi$
$251$		−	3044.59i		−	0.765630i	0.923825	−	0.382815i	$-0.125045\pi$
$252$	−767.260	+	2070.22i	−0.191797	+	0.517506i
$253$	1754.73	+	1754.73i	0.436042	+	0.436042i
$254$	2340.89			0.578271
$255$	−3639.04	−	3822.54i	−0.893668	−	0.938732i
$256$	5286.74			1.29071
$257$	946.317	+	946.317i	0.229687	+	0.229687i	0.812562	−	0.582875i	$-0.198072\pi$
$257$	946.317	+	946.317i	0.229687	+	0.229687i	−0.582875	+	0.812562i	$0.698072\pi$
$258$	−2634.64	+	4108.95i	−0.635758	+	0.991521i
$259$			3023.26i			0.725314i
$260$	−65.4670	+	267.724i	−0.0156157	+	0.0638598i
$261$	569.040	+	1239.21i	0.134953	+	0.293889i
$262$	3725.72	−	3725.72i	0.878532	−	0.878532i
$263$	−67.0257	+	67.0257i	−0.0157148	+	0.0157148i	−0.714921	−	0.699206i	$-0.753537\pi$
$263$	−67.0257	+	67.0257i	−0.0157148	+	0.0157148i	0.699206	+	0.714921i	$0.253537\pi$
$264$	−259.792	−	1188.31i	−0.0605648	−	0.277027i
$265$	1294.11	−	5292.18i	0.299986	−	1.22678i
$266$		−	950.474i		−	0.219088i
$267$	5563.99	+	3567.60i	1.27532	+	0.817729i
$268$	2663.03	+	2663.03i	0.606979	+	0.606979i
$269$	−2658.15			−0.602492			−0.301246	−	0.953546i	$-0.597403\pi$
$269$	−2658.15			−0.602492			−0.301246	+	0.953546i	$0.597403\pi$
$270$	−2188.12	+	5486.13i	−0.493202	+	1.23657i
$271$	145.673			0.0326530			0.0163265	−	0.999867i	$-0.494803\pi$
$271$	145.673			0.0326530			0.0163265	+	0.999867i	$0.494803\pi$
$272$	4834.09	+	4834.09i	1.07761	+	1.07761i
$273$	−230.951	−	148.085i	−0.0512007	−	0.0328296i
$274$			5816.64i			1.28247i
$275$	−3785.66	−	1969.17i	−0.830123	−	0.431802i
$276$	498.478	+	2280.07i	0.108713	+	0.497261i
$277$	−1074.57	+	1074.57i	−0.233085	+	0.233085i	−0.813979	−	0.580894i	$-0.802703\pi$
$277$	−1074.57	+	1074.57i	−0.233085	+	0.233085i	0.580894	+	0.813979i	$0.302703\pi$
$278$	6652.34	−	6652.34i	1.43518	−	1.43518i
$279$	−1051.98	−	2290.93i	−0.225737	−	0.491592i
$280$	526.488	+	867.316i	0.112370	+	0.185115i
$281$		−	2020.29i		−	0.428898i	−0.976735	−	0.214449i	$-0.931204\pi$
$281$		−	2020.29i		−	0.428898i	0.976735	−	0.214449i	$-0.0687956\pi$
$282$	−571.802	+	891.776i	−0.120746	+	0.188314i
$283$	−2400.34	−	2400.34i	−0.504189	−	0.504189i	0.408548	−	0.912737i	$-0.366035\pi$
$283$	−2400.34	−	2400.34i	−0.504189	−	0.504189i	−0.912737	+	0.408548i	$0.866035\pi$
$284$	−4534.49			−0.947438
$285$	27.2420	−	1107.73i	0.00566202	−	0.230233i
$286$	−512.844			−0.106032
$287$	830.913	+	830.913i	0.170896	+	0.170896i
$288$	2144.05	−	5785.06i	0.438678	−	1.18364i
$289$			3340.15i			0.679860i
$290$	−2065.35	−	505.042i	−0.418212	−	0.102266i
$291$	3102.09	−	678.191i	0.624906	−	0.136619i
$292$	2150.71	−	2150.71i	0.431031	−	0.431031i
$293$	−2533.13	+	2533.13i	−0.505075	+	0.505075i	−0.913011	−	0.407936i	$-0.866249\pi$
$293$	−2533.13	+	2533.13i	−0.505075	+	0.505075i	0.407936	+	0.913011i	$0.366249\pi$
$294$	−3208.62	+	701.482i	−0.636499	+	0.139154i
$295$	−4024.89	+	2443.23i	−0.794366	+	0.482204i
$296$		−	1566.53i		−	0.307611i
$297$	−4742.71	−	666.830i	−0.926598	−	0.130281i
$298$	−9506.54	−	9506.54i	−1.84798	−	1.84798i
$299$	−290.018			−0.0560943
$300$	−1997.57	−	3480.87i	−0.384432	−	0.669893i
$301$	3301.42			0.632196
$302$	−7154.79	−	7154.79i	−1.36328	−	1.36328i
$303$	−4662.27	+	7271.21i	−0.883961	+	1.37861i
$304$			1435.32i			0.270794i
$305$	19.1146	−	11.6031i	0.00358852	−	0.00217834i
$306$	8393.59	−	3854.31i	1.56807	−	0.720052i
$307$	3159.93	−	3159.93i	0.587449	−	0.587449i	−0.349491	−	0.936940i	$-0.613645\pi$
$307$	3159.93	−	3159.93i	0.587449	−	0.587449i	0.936940	+	0.349491i	$0.113645\pi$
$308$	1973.87	−	1973.87i	0.365167	−	0.365167i
$309$	1215.56	+	5560.03i	0.223788	+	1.02362i
$310$	3818.21	+	933.673i	0.699548	+	0.171061i
$311$			7206.19i			1.31391i	0.753931	+	0.656954i	$0.228155\pi$
$311$			7206.19i			1.31391i	−0.753931	+	0.656954i	$0.771845\pi$
$312$	119.670	+	76.7315i	0.0217146	+	0.0139233i
$313$	2029.31	+	2029.31i	0.366464	+	0.366464i	0.866186	−	0.499722i	$-0.166564\pi$
$313$	2029.31	+	2029.31i	0.366464	+	0.366464i	−0.499722	+	0.866186i	$0.666564\pi$
$314$	9641.19			1.73275
$315$	3922.54	−	757.026i	0.701619	−	0.135408i
$316$	−3633.31			−0.646804
$317$	689.223	+	689.223i	0.122116	+	0.122116i	0.765524	−	0.643408i	$-0.222480\pi$
$317$	689.223	+	689.223i	0.122116	+	0.122116i	−0.643408	+	0.765524i	$0.722480\pi$
$318$	8026.21	+	5146.37i	1.41537	+	0.907528i
$319$		−	1724.09i		−	0.302603i
$320$	1499.18	+	2469.69i	0.261895	+	0.431437i
$321$	−1836.70	−	8401.16i	−0.319360	−	1.46077i
$322$	2561.47	−	2561.47i	0.443308	−	0.443308i
$323$	−1225.25	+	1225.25i	−0.211067	+	0.211067i
$324$	−3416.44	−	2935.61i	−0.585809	−	0.503363i
$325$	475.574	−	150.113i	0.0811696	−	0.0256208i
$326$			14266.6i			2.42378i
$327$	−3546.84	+	5531.60i	−0.599818	+	0.935469i
$328$	−430.546	−	430.546i	−0.0724784	−	0.0724784i
$329$	716.516			0.120069
$330$	5408.72	−	5149.08i	0.902243	−	0.858932i
$331$	−8226.53			−1.36608			−0.683038	−	0.730383i	$-0.739342\pi$
$331$	−8226.53			−1.36608			−0.683038	+	0.730383i	$0.739342\pi$
$332$	−1346.99	−	1346.99i	−0.222667	−	0.222667i
$333$	−5783.64	−	2143.52i	−0.951777	−	0.352745i
$334$			743.096i			0.121738i
$335$	1618.67	−	6619.47i	0.263992	−	1.07958i
$336$	−5055.37	+	1105.23i	−0.820813	+	0.179449i
$337$	1777.34	−	1777.34i	0.287294	−	0.287294i	−0.548715	−	0.836009i	$-0.684883\pi$
$337$	1777.34	−	1777.34i	0.287294	−	0.287294i	0.836009	+	0.548715i	$0.184883\pi$
$338$	−5807.36	+	5807.36i	−0.934552	+	0.934552i
$339$	2736.41	−	598.245i	0.438411	−	0.0958472i
$340$	−1490.73	+	6096.29i	−0.237784	+	0.972405i
$341$			3187.32i			0.506168i
$342$	1818.30	+	673.895i	0.287493	+	0.106550i
$343$	4780.56	+	4780.56i	0.752554	+	0.752554i
$344$	−1710.66			−0.268119
$345$	3058.69	−	2911.86i	0.477316	−	0.454403i
$346$	−4694.77			−0.729458
$347$	1715.22	+	1715.22i	0.265354	+	0.265354i	0.827225	−	0.561871i	$-0.189918\pi$
$347$	1715.22	+	1715.22i	0.265354	+	0.265354i	−0.561871	+	0.827225i	$0.689918\pi$
$348$	875.242	−	1365.02i	0.134821	−	0.210266i
$349$		−	8603.96i		−	1.31965i	−0.751417	−	0.659827i	$-0.770629\pi$
$349$		−	8603.96i		−	1.31965i	0.751417	−	0.659827i	$-0.229371\pi$
$350$	−2874.51	+	5526.13i	−0.438997	+	0.843954i
$351$	447.039	−	336.827i	0.0679806	−	0.0512208i
$352$	−5515.81	+	5515.81i	−0.835209	+	0.835209i
$353$	5425.13	−	5425.13i	0.817990	−	0.817990i	−0.167827	−	0.985816i	$-0.553675\pi$
$353$	5425.13	−	5425.13i	0.817990	−	0.817990i	0.985816	+	0.167827i	$0.0536750\pi$
$354$	−1759.87	−	8049.77i	−0.264227	−	1.20859i
$355$	4257.57	+	7013.77i	0.636531	+	1.04860i
$356$		−	7859.58i		−	1.17010i
$357$	−5258.93	−	3372.00i	−0.779642	−	0.499903i
$358$	6690.76	+	6690.76i	0.987759	+	0.987759i
$359$	11418.9			1.67874			0.839370	−	0.543560i	$-0.182924\pi$
$359$	11418.9			1.67874			0.839370	+	0.543560i	$0.182924\pi$
$360$	−2032.50	+	392.260i	−0.297562	+	0.0574276i
$361$	6495.20			0.946961
$362$	−718.361	−	718.361i	−0.104299	−	0.104299i
$363$	−724.510	−	464.552i	−0.104757	−	0.0671699i
$364$			326.237i			0.0469766i
$365$	−5346.01	−	1307.27i	−0.766638	−	0.187467i
$366$	8.35782	+	38.2292i	0.00119363	+	0.00545976i
$367$	6554.73	−	6554.73i	0.932299	−	0.932299i	−0.0655499	−	0.997849i	$-0.520880\pi$
$367$	6554.73	−	6554.73i	0.932299	−	0.932299i	0.997849	+	0.0655499i	$0.0208802\pi$
$368$	−3868.11	+	3868.11i	−0.547932	+	0.547932i
$369$	−2178.70	+	1000.45i	−0.307368	+	0.141142i
$370$	8221.34	−	4990.60i	1.15515	−	0.701214i
$371$		−	6448.83i		−	0.902443i
$372$	−1618.06	+	2523.51i	−0.225518	+	0.351714i
$373$	−5967.46	−	5967.46i	−0.828374	−	0.828374i	0.158918	−	0.987292i	$-0.449199\pi$
$373$	−5967.46	−	5967.46i	−0.828374	−	0.828374i	−0.987292	+	0.158918i	$0.949199\pi$
$374$	−11677.8			−1.61456
$375$	−3508.49	+	6358.06i	−0.483140	+	0.875543i
$376$	−371.270			−0.0509222
$377$	142.477	+	142.477i	0.0194640	+	0.0194640i
$378$	−973.408	+	6923.18i	−0.132452	+	0.942037i
$379$		−	1680.48i		−	0.227758i	−0.993495	−	0.113879i	$-0.963672\pi$
$379$		−	1680.48i		−	0.227758i	0.993495	−	0.113879i	$-0.0363276\pi$
$380$	−1126.36	+	683.733i	−0.152055	+	0.0923020i
$381$	3155.76	−	689.925i	0.424342	−	0.0927715i
$382$	−6444.09	+	6444.09i	−0.863110	+	0.863110i
$383$	7493.42	−	7493.42i	0.999728	−	0.999728i	−0.000271480	−	1.00000i	$-0.500086\pi$
$383$	7493.42	−	7493.42i	0.999728	−	0.999728i	1.00000		0.000271480i	$8.64148e-5\pi$
$384$	4340.16	−	948.864i	0.576779	−	0.126098i
$385$	−4906.42	−	1199.77i	−0.649492	−	0.158821i
$386$		−	10465.5i		−	1.38000i
$387$	−2340.74	+	6315.78i	−0.307459	+	0.829584i
$388$	−2669.98	−	2669.98i	−0.349349	−	0.349349i
$389$	−7966.97			−1.03841			−0.519205	−	0.854650i	$-0.673772\pi$
$389$	−7966.97			−1.03841			−0.519205	+	0.854650i	$0.673772\pi$
$390$	−21.4567	+	872.487i	−0.00278591	+	0.113282i
$391$	−6603.94			−0.854158
$392$	−813.939	−	813.939i	−0.104873	−	0.104873i
$393$	3924.57	−	6120.71i	0.503736	−	0.785620i
$394$		−	4433.78i		−	0.566930i
$395$	3411.43	+	5619.87i	0.434551	+	0.715864i
$396$	2376.61	+	5175.59i	0.301589	+	0.656776i
$397$	−8188.88	+	8188.88i	−1.03523	+	1.03523i	−0.0358786	+	0.999356i	$0.511423\pi$
$397$	−8188.88	+	8188.88i	−1.03523	+	1.03523i	−0.999356	+	0.0358786i	$0.988577\pi$
$398$	4101.85	−	4101.85i	0.516601	−	0.516601i
$399$	−280.130	−	1281.33i	−0.0351480	−	0.160769i
$400$	4340.83	−	8345.08i	0.542604	−	1.04313i
$401$			5167.66i			0.643542i	0.946817	+	0.321771i	$0.104278\pi$
$401$			5167.66i			0.643542i	−0.946817	+	0.321771i	$0.895722\pi$
$402$	10039.2	+	6437.08i	1.24555	+	0.798638i
$403$	−263.398	−	263.398i	−0.0325577	−	0.0325577i
$404$	10271.2			1.26488
$405$	−1332.89	+	8040.74i	−0.163535	+	0.986537i
$406$	−2516.74			−0.307645
$407$	5514.46	+	5514.46i	0.671601	+	0.671601i
$408$	2724.97	+	1747.24i	0.330652	+	0.212012i
$409$			8514.82i			1.02941i	0.857366	+	0.514707i	$0.172099\pi$
$409$			8514.82i			1.02941i	−0.857366	+	0.514707i	$0.827901\pi$
$410$	887.935	−	3631.17i	0.106956	−	0.437392i
$411$	1714.32	+	7841.41i	0.205745	+	0.941090i
$412$	4785.54	−	4785.54i	0.572249	−	0.572249i
$413$	−3940.88	+	3940.88i	−0.469535	+	0.469535i
$414$	3084.11	+	6716.32i	0.366125	+	0.797316i
$415$	−818.738	+	3348.19i	−0.0968440	+	0.396039i
$416$		−	911.644i		−	0.107445i
$417$	7007.39	−	10928.6i	0.822910	−	1.28340i
$418$	−1733.67	−	1733.67i	−0.202863	−	0.202863i
$419$	−11939.7			−1.39211			−0.696053	−	0.717990i	$-0.745062\pi$
$419$	−11939.7			−1.39211			−0.696053	+	0.717990i	$0.745062\pi$
$420$	−3275.50	−	3440.67i	−0.380543	−	0.399732i
$421$	10873.3			1.25875			0.629373	−	0.777103i	$-0.283312\pi$
$421$	10873.3			1.25875			0.629373	+	0.777103i	$0.283312\pi$
$422$	29.1236	+	29.1236i	0.00335951	+	0.00335951i
$423$	−508.016	+	1370.73i	−0.0583938	+	0.157558i
$424$			3341.52i			0.382733i
$425$	10829.2	−	3418.19i	1.23598	−	0.390133i
$426$	−14027.5	+	3066.76i	−1.59539	+	0.348791i
$427$	18.7156	−	18.7156i	0.00212111	−	0.00212111i
$428$	−7230.91	+	7230.91i	−0.816634	+	0.816634i
$429$	−691.364	+	151.149i	−0.0778074	+	0.0170106i
$430$	−5449.77	−	8977.76i	−0.611189	−	1.00685i
$431$		−	7603.48i		−	0.849760i	−0.905250	−	0.424880i	$-0.860316\pi$
$431$		−	7603.48i		−	0.849760i	0.905250	−	0.424880i	$-0.139684\pi$
$432$	1469.95	−	10454.8i	0.163711	−	1.16437i
$433$	4681.19	+	4681.19i	0.519547	+	0.519547i	0.917434	−	0.397887i	$-0.130257\pi$
$433$	4681.19	+	4681.19i	0.519547	+	0.519547i	−0.397887	+	0.917434i	$0.630257\pi$
$434$	4652.70			0.514601
$435$	−2933.14	−	72.1336i	−0.323295	−	0.00795067i
$436$	7813.84			0.858292
$437$	−980.409	−	980.409i	−0.107321	−	0.107321i
$438$	5198.71	−	8107.85i	0.567133	−	0.884493i
$439$		−	8608.08i		−	0.935857i	−0.883766	−	0.467929i	$-0.845000\pi$
$439$		−	8608.08i		−	0.935857i	0.883766	−	0.467929i	$-0.155000\pi$
$440$	2542.31	+	621.675i	0.275454	+	0.0673572i
$441$	−4118.80	+	1891.34i	−0.444746	+	0.204226i
$442$	965.047	−	965.047i	0.103852	−	0.103852i
$443$	−6466.81	+	6466.81i	−0.693561	+	0.693561i	−0.963014	−	0.269453i	$-0.913157\pi$
$443$	−6466.81	+	6466.81i	−0.693561	+	0.693561i	0.269453	+	0.963014i	$0.413157\pi$
$444$	1566.53	+	7165.42i	0.167442	+	0.765891i
$445$	−12156.9	+	7379.61i	−1.29504	+	0.786128i
$446$		−	4427.97i		−	0.470113i
$447$	−15617.6	−	10013.9i	−1.65254	−	1.05960i
$448$	2418.14	+	2418.14i	0.255014	+	0.255014i
$449$	−356.370			−0.0374569			−0.0187284	−	0.999825i	$-0.505962\pi$
$449$	−356.370			−0.0374569			−0.0187284	+	0.999825i	$0.505962\pi$
$450$	−8533.70	−	9417.15i	−0.893961	−	0.986508i
$451$	3031.19			0.316481
$452$	−2355.24	−	2355.24i	−0.245091	−	0.245091i
$453$	−11754.1	−	7536.66i	−1.21911	−	0.781685i
$454$			18325.0i			1.89435i
$455$	504.611	−	306.314i	0.0519923	−	0.0315609i
$456$	145.152	+	663.935i	0.0149065	+	0.0681834i
$457$	1512.80	−	1512.80i	0.154849	−	0.154849i	−0.625431	−	0.780280i	$-0.715077\pi$
$457$	1512.80	−	1512.80i	0.154849	−	0.154849i	0.780280	+	0.625431i	$0.215077\pi$
$458$	−4474.19	+	4474.19i	−0.456474	+	0.456474i
$459$	10179.4	−	7669.81i	1.03515	−	0.779948i
$460$	−4878.08	−	1192.84i	−0.494438	−	0.120906i
$461$			13307.9i			1.34449i	0.740327	+	0.672246i	$0.234670\pi$
$461$			13307.9i			1.34449i	−0.740327	+	0.672246i	$0.765330\pi$
$462$	4771.23	−	7441.16i	0.480472	−	0.749338i
$463$	−1237.43	−	1237.43i	−0.124208	−	0.124208i	0.642270	−	0.766478i	$-0.277993\pi$
$463$	−1237.43	−	1237.43i	−0.124208	−	0.124208i	−0.766478	+	0.642270i	$0.777993\pi$
$464$	3800.56			0.380251
$465$	5422.51	+	133.353i	0.540780	+	0.0132992i
$466$	11218.8			1.11524
$467$	−8201.87	−	8201.87i	−0.812713	−	0.812713i	0.172327	−	0.985040i	$-0.444872\pi$
$467$	−8201.87	−	8201.87i	−0.812713	−	0.812713i	−0.985040	+	0.172327i	$0.944872\pi$
$468$	−624.107	−	231.305i	−0.0616439	−	0.0228463i
$469$		−	8066.19i		−	0.794162i
$470$	−1182.78	−	1948.46i	−0.116080	−	0.191225i
$471$	12997.3	−	2841.52i	1.27151	−	0.277984i
$472$	2042.01	−	2042.01i	0.199133	−	0.199133i
$473$	6021.83	−	6021.83i	0.585378	−	0.585378i
$474$	−11239.7	+	2457.28i	−1.08915	+	0.238115i
$475$	2115.14	+	1100.23i	0.204314	+	0.106278i
$476$			7428.67i			0.715321i
$477$	12336.9	+	4572.28i	1.18421	+	0.438889i
$478$	−695.273	−	695.273i	−0.0665294	−	0.0665294i
$479$	−11419.1			−1.08926			−0.544629	−	0.838677i	$-0.683329\pi$
$479$	−11419.1			−1.08926			−0.544629	+	0.838677i	$0.683329\pi$
$480$	9153.13	+	9614.68i	0.870378	+	0.914267i
$481$	−911.420			−0.0863974
$482$	15979.5	+	15979.5i	1.51005	+	1.51005i
$483$	2698.18	−	4208.05i	0.254185	−	0.396424i
$484$			1023.43i			0.0961147i
$485$	−1622.89	+	6636.73i	−0.151942	+	0.621358i
$486$	−12554.2	−	6770.77i	−1.17175	−	0.631952i
$487$	−6066.93	+	6066.93i	−0.564515	+	0.564515i	−0.930587	−	0.366071i	$-0.880703\pi$
$487$	−6066.93	+	6066.93i	−0.564515	+	0.564515i	0.366071	+	0.930587i	$0.380703\pi$
$488$	−9.69769	+	9.69769i	−0.000899577	+	0.000899577i
$489$	4204.74	+	19232.7i	0.388845	+	1.77860i
$490$	1678.63	−	6864.66i	0.154760	−	0.632885i
$491$			8978.88i			0.825277i	0.910895	+	0.412639i	$0.135393\pi$
$491$			8978.88i			0.825277i	−0.910895	+	0.412639i	$0.864607\pi$
$492$	2399.89	+	1538.80i	0.219909	+	0.141005i
$493$	3244.31	+	3244.31i	0.296382	+	0.296382i
$494$	286.538			0.0260971
$495$	5773.92	−	8535.57i	0.524280	−	0.775041i
$496$	−7026.11			−0.636051
$497$	6867.38	+	6867.38i	0.619807	+	0.619807i
$498$	−5077.92	−	3255.94i	−0.456922	−	0.292976i
$499$		−	7674.34i		−	0.688478i	−0.938882	−	0.344239i	$-0.888137\pi$
$499$		−	7674.34i		−	0.688478i	0.938882	−	0.344239i	$-0.111863\pi$
$500$	8616.53	−	568.849i	0.770686	−	0.0508794i
$501$	219.010	+	1001.77i	0.0195303	+	0.0893326i
$502$	−8106.54	+	8106.54i	−0.720743	+	0.720743i
$503$	4044.23	−	4044.23i	0.358496	−	0.358496i	−0.504762	−	0.863258i	$-0.668420\pi$
$503$	4044.23	−	4044.23i	0.358496	−	0.358496i	0.863258	+	0.504762i	$0.168420\pi$
$504$	−2226.69	+	1022.49i	−0.196795	+	0.0903674i
$505$	−9643.93	−	15887.1i	−0.849800	−	1.39993i
$506$		−	9344.28i		−	0.820957i
$507$	−6117.31	+	9540.48i	−0.535857	+	0.835715i
$508$	−2716.17	−	2716.17i	−0.237226	−	0.237226i
$509$	12532.5			1.09134			0.545672	−	0.837999i	$-0.316275\pi$
$509$	12532.5			1.09134			0.545672	+	0.837999i	$0.316275\pi$
$510$	−488.586	+	19867.2i	−0.0424215	+	1.72497i
$511$	−6514.42			−0.563955
$512$	−9239.91	−	9239.91i	−0.797559	−	0.797559i
$513$	2649.87	+	372.574i	0.228059	+	0.0320654i
$514$		−	5039.33i		−	0.432443i
$515$	−11895.4	−	2908.79i	−1.01781	−	0.248887i
$516$	7824.69	−	1710.66i	0.667563	−	0.145945i
$517$	1306.93	−	1306.93i	0.111177	−	0.111177i
$518$	8049.75	−	8049.75i	0.682791	−	0.682791i
$519$	−6329.02	+	1383.68i	−0.535285	+	0.117026i
$520$	−261.469	+	158.720i	−0.0220503	+	0.0133852i
$521$		−	19201.8i		−	1.61468i	−0.590089	−	0.807338i	$-0.700907\pi$
$521$		−	19201.8i		−	1.61468i	0.590089	−	0.807338i	$-0.299093\pi$
$522$	1784.39	−	4814.65i	0.149618	−	0.403700i
$523$	5472.69	+	5472.69i	0.457560	+	0.457560i	0.897854	−	0.440294i	$-0.145126\pi$
$523$	5472.69	+	5472.69i	0.457560	+	0.457560i	−0.440294	+	0.897854i	$0.645126\pi$
$524$	−8646.00			−0.720806
$525$	−2246.42	+	8296.97i	−0.186747	+	0.689732i
$526$	356.926			0.0295869
$527$	−5997.77	−	5997.77i	−0.495762	−	0.495762i
$528$	−7205.10	+	11237.0i	−0.593867	+	0.926187i
$529$			6882.71i			0.565687i
$530$	−17536.7	+	10645.3i	−1.43725	+	0.872457i
$531$	−4744.97	−	10333.2i	−0.387786	−	0.844488i
$532$	−1102.85	+	1102.85i	−0.0898769	+	0.0898769i
$533$	−250.495	+	250.495i	−0.0203567	+	0.0203567i
$534$	−5315.58	−	24313.8i	−0.430763	−	1.97034i
$535$	17973.8	+	4395.16i	1.45248	+	0.355176i
$536$			4179.58i			0.336810i
$537$	10991.8	+	7047.87i	0.883295	+	0.566365i
$538$	7077.60	+	7077.60i	0.567169	+	0.567169i
$539$	5730.40			0.457933
$540$	8904.53	−	3826.73i	0.709611	−	0.304956i
$541$	12778.2			1.01548			0.507741	−	0.861510i	$-0.330481\pi$
$541$	12778.2			1.01548			0.507741	+	0.861510i	$0.330481\pi$
$542$	−387.868	−	387.868i	−0.0307387	−	0.0307387i
$543$	−1180.14	−	756.702i	−0.0932684	−	0.0598033i
$544$		−	20758.8i		−	1.63608i
$545$	−7336.66	−	12086.1i	−0.576638	−	0.949933i
$546$	220.640	+	1009.22i	0.0172940	+	0.0791038i
$547$	−2414.12	+	2414.12i	−0.188702	+	0.188702i	−0.795135	−	0.606433i	$-0.792600\pi$
$547$	−2414.12	+	2414.12i	−0.188702	+	0.188702i	0.606433	+	0.795135i	$0.292600\pi$
$548$	6749.12	−	6749.12i	0.526110	−	0.526110i
$549$	22.5343	+	49.0735i	0.00175181	+	0.00381494i
$550$	4836.58	+	15322.8i	0.374968	+	1.18794i
$551$			963.290i			0.0744783i
$552$	−1398.09	+	2180.44i	−0.107802	+	0.168126i
$553$	5502.57	+	5502.57i	0.423134	+	0.423134i
$554$	5722.30			0.438840
$555$	9612.32	−	9150.88i	0.735171	−	0.699880i
$556$	−15437.6			−1.17752
$557$	−5573.05	−	5573.05i	−0.423946	−	0.423946i	0.462614	−	0.886560i	$-0.346912\pi$
$557$	−5573.05	−	5573.05i	−0.423946	−	0.423946i	−0.886560	+	0.462614i	$0.846912\pi$
$558$	−3298.81	+	8900.85i	−0.250268	+	0.675274i
$559$			995.277i			0.0753054i
$560$	2644.77	−	10815.7i	0.199575	−	0.816153i
$561$	−15742.9	+	3441.78i	−1.18479	+	0.259023i
$562$	−5379.23	+	5379.23i	−0.403753	+	0.403753i
$563$	−3488.75	+	3488.75i	−0.261160	+	0.261160i	−0.825525	−	0.564365i	$-0.809121\pi$
$563$	−3488.75	+	3488.75i	−0.261160	+	0.261160i	0.564365	+	0.825525i	$0.309121\pi$
$564$	1698.21	−	371.270i	0.126786	−	0.0277186i
$565$	−1431.58	+	5854.39i	−0.106597	+	0.435922i
$566$			12782.3i			0.949260i
$567$	728.199	+	9620.03i	0.0539356	+	0.712528i
$568$	−3558.40	−	3558.40i	−0.262865	−	0.262865i
$569$	4924.15			0.362796			0.181398	−	0.983410i	$-0.441938\pi$
$569$	4924.15			0.362796			0.181398	+	0.983410i	$0.441938\pi$
$570$	−3021.99	+	2876.92i	−0.222065	+	0.211405i
$571$	−5642.12			−0.413512			−0.206756	−	0.978393i	$-0.566291\pi$
$571$	−5642.12			−0.413512			−0.206756	+	0.978393i	$0.566291\pi$
$572$	595.059	+	595.059i	0.0434977	+	0.0434977i
$573$	−6788.02	+	10586.5i	−0.494893	+	0.771829i
$574$		−	4424.78i		−	0.321754i
$575$	2735.14	+	8665.22i	0.198371	+	0.628460i
$576$	−6340.50	+	2911.53i	−0.458659	+	0.210614i
$577$	8505.39	−	8505.39i	0.613663	−	0.613663i	−0.330235	−	0.943899i	$-0.607128\pi$
$577$	8505.39	−	8505.39i	0.613663	−	0.613663i	0.943899	+	0.330235i	$0.107128\pi$
$578$	8893.50	−	8893.50i	0.640002	−	0.640002i
$579$	−3084.47	−	14108.6i	−0.221392	−	1.01266i
$580$	1810.44	+	2982.46i	0.129611	+	0.213517i
$581$			4079.96i			0.291334i
$582$	−10065.4	−	6453.87i	−0.716879	−	0.459659i
$583$	−11762.7	−	11762.7i	−0.835612	−	0.835612i
$584$	3375.51			0.239177
$585$	228.220	+	1182.52i	0.0161295	+	0.0835750i
$586$	13489.4			0.950927
$587$	1464.72	+	1464.72i	0.102990	+	0.102990i	0.756724	−	0.653734i	$-0.226798\pi$
$587$	1464.72	+	1464.72i	0.102990	+	0.102990i	−0.653734	+	0.756724i	$0.726798\pi$
$588$	4536.95	+	2909.07i	0.318198	+	0.204027i
$589$		−	1780.84i		−	0.124581i
$590$	17222.0	+	4211.33i	1.20173	+	0.293860i
$591$	−1306.75	−	5977.17i	−0.0909521	−	0.416020i
$592$	−12156.0	+	12156.0i	−0.843935	+	0.843935i
$593$	−18086.4	+	18086.4i	−1.25248	+	1.25248i	−0.297871	+	0.954606i	$0.596277\pi$
$593$	−18086.4	+	18086.4i	−1.25248	+	1.25248i	−0.954606	+	0.297871i	$0.903723\pi$
$594$	10852.4	+	14403.4i	0.749631	+	0.994917i
$595$	11490.4	−	6975.01i	0.791697	−	0.480584i
$596$			22061.1i			1.51621i
$597$	4320.78	−	6738.63i	0.296211	−	0.461966i
$598$	772.204	+	772.204i	0.0528056	+	0.0528056i
$599$	21899.3			1.49379			0.746897	−	0.664940i	$-0.231543\pi$
$599$	21899.3			1.49379			0.746897	+	0.664940i	$0.231543\pi$
$600$	1164.01	−	4299.16i	0.0792006	−	0.292520i
$601$	−12431.8			−0.843766			−0.421883	−	0.906650i	$-0.638631\pi$
$601$	−12431.8			−0.843766			−0.421883	+	0.906650i	$0.638631\pi$
$602$	−8790.38	−	8790.38i	−0.595132	−	0.595132i
$603$	15431.0	+	5719.00i	1.04212	+	0.386229i
$604$			16603.6i			1.11853i
$605$	1583.00	−	960.930i	0.106377	−	0.0645741i
$606$	31774.1	−	6946.59i	2.12993	−	0.465653i
$607$	8237.79	−	8237.79i	0.550843	−	0.550843i	−0.375841	−	0.926684i	$-0.622646\pi$
$607$	8237.79	−	8237.79i	0.550843	−	0.550843i	0.926684	+	0.375841i	$0.122646\pi$
$608$	3081.82	−	3081.82i	0.205566	−	0.205566i
$609$	−3392.82	+	741.752i	−0.225754	+	0.0493552i
$610$	−81.7891	−	20.0000i	−0.00542876	−	0.00132750i
$611$			216.007i			0.0143023i
$612$	−14211.4	−	5267.00i	−0.938663	−	0.347885i
$613$	−8913.02	−	8913.02i	−0.587265	−	0.587265i	0.349625	−	0.936890i	$-0.386309\pi$
$613$	−8913.02	−	8913.02i	−0.587265	−	0.587265i	−0.936890	+	0.349625i	$0.886309\pi$
$614$	−16827.3			−1.10602
$615$	126.821	−	5156.88i	0.00831530	−	0.338123i
$616$	3097.95			0.202630
$617$	−1378.18	−	1378.18i	−0.0899244	−	0.0899244i	0.660714	−	0.750638i	$-0.270254\pi$
$617$	−1378.18	−	1378.18i	−0.0899244	−	0.0899244i	−0.750638	+	0.660714i	$0.770254\pi$
$618$	11567.6	−	18040.7i	0.752941	−	1.17428i
$619$			18926.2i			1.22893i	0.788945	+	0.614464i	$0.210628\pi$
$619$			18926.2i			1.22893i	−0.788945	+	0.614464i	$0.789372\pi$
$620$	−3346.97	−	5513.67i	−0.216802	−	0.357152i
$621$	6137.16	+	8145.29i	0.396580	+	0.526344i
$622$	19187.2	−	19187.2i	1.23688	−	1.23688i
$623$	−11903.2	+	11903.2i	−0.765474	+	0.765474i
$624$	−333.191	−	1524.04i	−0.0213755	−	0.0977730i
$625$	−8970.20	−	12793.6i	−0.574093	−	0.818790i
$626$		−	10806.5i		−	0.689959i
$627$	−2848.12	−	1826.20i	−0.181408	−	0.116318i
$628$	−11186.8	−	11186.8i	−0.710831	−	0.710831i
$629$	−20753.7			−1.31559
$630$	−12459.8	−	8428.50i	−0.787954	−	0.533015i
$631$	−26118.8			−1.64782			−0.823909	−	0.566723i	$-0.808211\pi$
$631$	−26118.8			−1.64782			−0.823909	+	0.566723i	$0.808211\pi$
$632$	−2851.21	−	2851.21i	−0.179454	−	0.179454i
$633$	47.8450	+	30.6780i	0.00300421	+	0.00192629i
$634$		−	3670.26i		−	0.229912i
$635$	−1650.97	+	6751.56i	−0.103176	+	0.421933i
$636$	−3341.52	−	15284.3i	−0.208333	−	0.952929i
$637$	−473.556	+	473.556i	−0.0294552	+	0.0294552i
$638$	−4590.56	+	4590.56i	−0.284862	+	0.284862i
$639$	−18006.7	+	8268.59i	−1.11476	+	0.511894i
$640$	−2270.60	+	9285.53i	−0.140240	+	0.573504i
$641$		−	15846.5i		−	0.976442i	−0.872720	−	0.488221i	$-0.837646\pi$
$641$		−	15846.5i		−	0.976442i	0.872720	−	0.488221i	$-0.162354\pi$
$642$	−17478.6	+	27259.4i	−1.07449	+	1.67577i
$643$	89.9404	+	89.9404i	0.00551618	+	0.00551618i	0.709859	−	0.704343i	$-0.248758\pi$
$643$	89.9404	+	89.9404i	0.00551618	+	0.00551618i	−0.704343	+	0.709859i	$0.748758\pi$
$644$	−5944.21			−0.363719
$645$	−9992.83	−	10496.7i	−0.610027	−	0.640787i
$646$	6524.70			0.397385
$647$	20057.0	+	20057.0i	1.21874	+	1.21874i	0.968074	+	0.250665i	$0.0806492\pi$
$647$	20057.0	+	20057.0i	1.21874	+	1.21874i	0.250665	+	0.968074i	$0.419351\pi$
$648$	−377.323	−	4984.71i	−0.0228745	−	0.302188i
$649$			14376.4i			0.869527i
$650$	−1665.96	−	866.575i	−0.100530	−	0.0522921i
$651$	6272.31	−	1371.28i	0.377621	−	0.0825570i
$652$	16553.7	−	16553.7i	0.994313	−	0.994313i
$653$	20478.4	−	20478.4i	1.22723	−	1.22723i	0.262225	−	0.965007i	$-0.415544\pi$
$653$	20478.4	−	20478.4i	1.22723	−	1.22723i	0.965007	−	0.262225i	$-0.0844562\pi$
$654$	24172.3	−	5284.64i	1.44528	−	0.315972i
$655$	8117.99	+	13373.3i	0.484269	+	0.797767i
$656$			6681.92i			0.397691i
$657$	4618.78	−	12462.4i	0.274271	−	0.740036i
$658$	−1907.80	−	1907.80i	−0.113030	−	0.113030i
$659$	−1169.87			−0.0691529			−0.0345765	−	0.999402i	$-0.511008\pi$
$659$	−1169.87			−0.0691529			−0.0345765	+	0.999402i	$0.511008\pi$
$660$	−12250.4	−	301.268i	−0.722492	−	0.0177679i
$661$	19622.6			1.15466			0.577329	−	0.816511i	$-0.304095\pi$
$661$	19622.6			1.15466			0.577329	+	0.816511i	$0.304095\pi$
$662$	21904.0	+	21904.0i	1.28599	+	1.28599i
$663$	1016.55	−	1585.41i	0.0595471	−	0.0928688i
$664$		−	2114.07i		−	0.123557i
$665$	2741.34	+	670.343i	0.159856	+	0.0390899i
$666$	9692.20	+	21106.9i	0.563912	+	1.22804i
$667$	−2596.01	+	2596.01i	−0.150701	+	0.150701i
$668$	862.224	−	862.224i	0.0499408	−	0.0499408i
$669$	−1305.04	−	5969.35i	−0.0754199	−	0.344975i
$670$	−21934.9	+	13315.1i	−1.26480	+	0.767774i
$671$		−	68.2750i		−	0.00392806i
$672$	13227.6	+	8481.46i	0.759323	+	0.486874i
$673$	15256.3	+	15256.3i	0.873830	+	0.873830i	0.992887	−	0.119057i	$-0.0379872\pi$
$673$	15256.3	+	15256.3i	0.873830	+	0.873830i	−0.119057	+	0.992887i	$0.537987\pi$
$674$	−9464.72			−0.540901
$675$	−14279.8	−	10180.1i	−0.814264	−	0.580495i
$676$	13476.7			0.766768
$677$	16.1429	+	16.1429i	0.000916428	+	0.000916428i	0.707565	−	0.706648i	$-0.249794\pi$
$677$	16.1429	+	16.1429i	0.000916428	+	0.000916428i	−0.706648	+	0.707565i	$0.749794\pi$
$678$	−8878.86	−	5693.08i	−0.502936	−	0.322480i
$679$			8087.23i			0.457083i
$680$	−5953.85	+	3614.17i	−0.335764	+	0.203819i
$681$	5400.87	+	24703.9i	0.303909	+	1.39010i
$682$	8486.57	−	8486.57i	0.476492	−	0.476492i
$683$	3894.05	−	3894.05i	0.218157	−	0.218157i	−0.589564	−	0.807722i	$-0.700700\pi$
$683$	3894.05	−	3894.05i	0.218157	−	0.218157i	0.807722	+	0.589564i	$0.200700\pi$
$684$	−1327.87	−	2891.73i	−0.0742287	−	0.161649i
$685$	−16776.2	−	4102.32i	−0.935747	−	0.228820i
$686$		−	25457.5i		−	1.41687i
$687$	−4712.99	+	7350.31i	−0.261735	+	0.408198i
$688$	13274.5	+	13274.5i	0.735587	+	0.735587i
$689$	1944.12			0.107497
$690$	−15897.2	−	390.953i	−0.877095	−	0.0215700i
$691$	−1041.11			−0.0573163			−0.0286581	−	0.999589i	$-0.509123\pi$
$691$	−1041.11			−0.0573163			−0.0286581	+	0.999589i	$0.509123\pi$
$692$	5447.40	+	5447.40i	0.299247	+	0.299247i
$693$	4238.99	−	11437.6i	0.232361	−	0.626955i
$694$		−	9133.91i		−	0.499594i
$695$	14494.8	+	23878.3i	0.791108	+	1.30324i
$696$	1758.02	−	384.346i	0.0957438	−	0.0209319i
$697$	−5703.96	+	5703.96i	−0.309975	+	0.309975i
$698$	−22908.9	+	22908.9i	−1.24229	+	1.24229i
$699$	15124.1	−	3306.49i	0.818378	−	0.178917i
$700$	9747.37	−	3076.71i	0.526309	−	0.166127i
$701$		−	29885.3i		−	1.61020i	−0.593138	−	0.805101i	$-0.702111\pi$
$701$		−	29885.3i		−	1.61020i	0.593138	−	0.805101i	$-0.297889\pi$
$702$	−2087.12	−	293.452i	−0.112213	−	0.0157773i
$703$	−3081.06	−	3081.06i	−0.165298	−	0.165298i
$704$	8821.42			0.472258
$705$	−2168.77	−	2278.13i	−0.115859	−	0.121701i
$706$	−28889.9			−1.54007
$707$	−15555.5	−	15555.5i	−0.827473	−	0.827473i
$708$	−7298.26	+	11382.3i	−0.387409	+	0.604198i
$709$			12115.0i			0.641734i	0.947124	+	0.320867i	$0.103974\pi$
$709$			12115.0i			0.641734i	−0.947124	+	0.320867i	$0.896026\pi$
$710$	7338.66	−	30011.1i	0.387908	−	1.58633i
$711$	−14428.1	+	6625.31i	−0.761033	+	0.349463i
$712$	6167.74	−	6167.74i	0.324643	−	0.324643i
$713$	4799.24	−	4799.24i	0.252080	−	0.252080i
$714$	5024.15	+	22980.8i	0.263339	+	1.20453i
$715$	361.695	−	1479.13i	0.0189183	−	0.0773657i
$716$		−	15526.8i		−	0.810422i
$717$	−1142.21	−	732.381i	−0.0594933	−	0.0381468i
$718$	−30404.1	−	30404.1i	−1.58032	−	1.58032i
$719$	6371.24			0.330469			0.165234	−	0.986254i	$-0.447162\pi$
$719$	6371.24			0.330469			0.165234	+	0.986254i	$0.447162\pi$
$720$	18815.7	+	12728.0i	0.973918	+	0.658811i
$721$	−14495.2			−0.748722
$722$	−17294.1	−	17294.1i	−0.891443	−	0.891443i
$723$	26251.5	+	16832.3i	1.35035	+	0.865839i
$724$			1667.05i			0.0855737i
$725$	2913.27	−	5600.64i	0.149236	−	0.286900i
$726$	692.164	+	3166.00i	0.0353838	+	0.161848i
$727$	15771.9	−	15771.9i	0.804604	−	0.804604i	−0.179207	−	0.983811i	$-0.557353\pi$
$727$	15771.9	−	15771.9i	0.804604	−	0.804604i	0.983811	+	0.179207i	$0.0573532\pi$
$728$	−256.012	+	256.012i	−0.0130336	+	0.0130336i
$729$	−18919.9	−	5427.61i	−0.961229	−	0.275751i
$730$	10753.6	+	17715.0i	0.545216	+	0.898168i
$731$			22663.2i			1.14669i
$732$	34.6601	−	54.0555i	0.00175010	−	0.00272944i
$733$	−5626.05	−	5626.05i	−0.283496	−	0.283496i	0.551005	−	0.834502i	$-0.314244\pi$
$733$	−5626.05	−	5626.05i	−0.283496	−	0.283496i	−0.834502	+	0.551005i	$0.814244\pi$
$734$	−34905.3			−1.75528
$735$	239.753	−	9748.98i	0.0120319	−	0.489247i
$736$	16610.6			0.831897
$737$	−14712.8	−	14712.8i	−0.735350	−	0.735350i
$738$	8464.82	+	3137.21i	0.422215	+	0.156480i
$739$		−	30340.1i		−	1.51026i	−0.655577	−	0.755129i	$-0.727574\pi$
$739$		−	30340.1i		−	1.51026i	0.655577	−	0.755129i	$-0.272426\pi$
$740$	−15330.0	−	3748.66i	−0.761543	−	0.186221i
$741$	386.282	−	84.4506i	0.0191504	−	0.00418674i
$742$	−17170.7	+	17170.7i	−0.849535	+	0.849535i
$743$	2368.77	−	2368.77i	0.116961	−	0.116961i	−0.646204	−	0.763165i	$-0.723645\pi$
$743$	2368.77	−	2368.77i	0.116961	−	0.116961i	0.763165	+	0.646204i	$0.223645\pi$
$744$	−3250.06	+	710.541i	−0.160152	+	0.0350130i
$745$	34123.3	−	20713.9i	1.67810	−	1.01866i
$746$			31778.0i			1.55962i
$747$	−7805.16	−	2892.73i	−0.382297	−	0.141686i
$748$	13550.0	+	13550.0i	0.662347	+	0.662347i
$749$	21902.1			1.06847
$750$	26270.7	−	7587.26i	1.27903	−	0.369397i
$751$	10606.2			0.515346			0.257673	−	0.966232i	$-0.417044\pi$
$751$	10606.2			0.515346			0.257673	+	0.966232i	$0.417044\pi$
$752$	2880.99	+	2880.99i	0.139706	+	0.139706i
$753$	−8539.21	+	13317.6i	−0.413262	+	0.644518i
$754$		−	758.720i		−	0.0366458i
$755$	25681.8	−	15589.6i	1.23796	−	0.751477i
$756$	9162.52	−	6903.60i	0.440790	−	0.332119i
$757$	−18470.4	+	18470.4i	−0.886812	+	0.886812i	−0.994215	−	0.107404i	$-0.965746\pi$
$757$	−18470.4	+	18470.4i	−0.886812	+	0.886812i	0.107404	+	0.994215i	$0.465746\pi$
$758$	−4474.44	+	4474.44i	−0.214405	+	0.214405i
$759$	−2754.01	−	12597.0i	−0.131705	−	0.602428i
$760$	−1420.45	−	347.345i	−0.0677963	−	0.0165783i
$761$			13568.0i			0.646307i	0.946347	+	0.323153i	$0.104743\pi$
$761$			13568.0i			0.646307i	−0.946347	+	0.323153i	$0.895257\pi$
$762$	−10239.5	−	6565.54i	−0.486797	−	0.312132i
$763$	−11833.9	−	11833.9i	−0.561488	−	0.561488i
$764$	14954.3			0.708152
$765$	5196.74	+	26927.0i	0.245606	+	1.27261i
$766$	−39904.0			−1.88223
$767$	−1188.05	−	1188.05i	−0.0559298	−	0.0559298i
$768$	−23125.2	−	14827.8i	−1.08654	−	0.696682i
$769$		−	11029.1i		−	0.517190i	−0.965986	−	0.258595i	$-0.916741\pi$
$769$		−	11029.1i		−	0.517190i	0.965986	−	0.258595i	$-0.0832594\pi$
$770$	9869.33	+	16258.4i	0.461904	+	0.760924i
$771$	−1485.23	−	6793.52i	−0.0693764	−	0.317332i
$772$	−12143.3	+	12143.3i	−0.566122	+	0.566122i
$773$	7090.94	−	7090.94i	0.329940	−	0.329940i	−0.522624	−	0.852563i	$-0.675047\pi$
$773$	7090.94	−	7090.94i	0.329940	−	0.329940i	0.852563	+	0.522624i	$0.175047\pi$
$774$	23048.9	−	10584.0i	1.07038	−	0.491515i
$775$	−5385.76	+	10353.9i	−0.249629	+	0.479902i
$776$		−	4190.48i		−	0.193852i
$777$	8479.38	−	13224.3i	0.391501	−	0.610580i
$778$	21212.9	+	21212.9i	0.977530	+	0.977530i
$779$	−1693.60			−0.0778940
$780$	1037.26	−	987.462i	0.0476150	−	0.0453293i
$781$	25052.3			1.14781
$782$	17583.7	+	17583.7i	0.804080	+	0.804080i
$783$	986.533	−	7016.53i	0.0450266	−	0.320243i
$784$			12632.1i			0.575440i
$785$	−6799.67	+	27806.9i	−0.309160	+	1.26430i
$786$	−26746.6	+	5847.45i	−1.21376	+	0.265358i
$787$	−17915.0	+	17915.0i	−0.811437	+	0.811437i	−0.984849	−	0.173412i	$-0.944521\pi$
$787$	−17915.0	+	17915.0i	−0.811437	+	0.811437i	0.173412	+	0.984849i	$0.444521\pi$
$788$	−5144.57	+	5144.57i	−0.232573	+	0.232573i
$789$	481.172	−	105.196i	0.0217112	−	0.00474660i
$790$	5880.19	−	24046.8i	0.264820	−	1.08297i
$791$			7133.90i			0.320673i
$792$	−2196.47	+	5926.52i	−0.0985458	+	0.265896i
$793$	5.64218	+	5.64218i	0.000252661	+	0.000252661i
$794$	43607.5			1.94908
$795$	−20503.7	+	19519.5i	−0.914707	+	0.870797i
$796$	−9518.87			−0.423854
$797$	−6043.79	−	6043.79i	−0.268610	−	0.268610i	0.559930	−	0.828540i	$-0.310828\pi$
$797$	−6043.79	−	6043.79i	−0.268610	−	0.268610i	−0.828540	+	0.559930i	$0.810828\pi$
$798$	−2665.81	+	4157.56i	−0.118256	+	0.184431i
$799$			4918.65i			0.217784i
$800$	−27238.3	+	8597.63i	−1.20377	+	0.379965i
$801$	−14331.9	−	31210.8i	−0.632199	−	1.37675i
$802$	13759.4	−	13759.4i	0.605813	−	0.605813i
$803$	−11882.3	+	11882.3i	−0.522191	+	0.522191i
$804$	−4179.58	−	19117.6i	−0.183336	−	0.838591i
$805$	5581.21	+	9194.28i	0.244362	+	0.402554i
$806$			1402.65i			0.0612979i
$807$	11627.3	+	7455.35i	0.507186	+	0.325205i
$808$	8060.22	+	8060.22i	0.350937	+	0.350937i
$809$	−35063.4			−1.52381			−0.761905	−	0.647689i	$-0.775736\pi$
$809$	−35063.4			−1.52381			−0.761905	+	0.647689i	$0.775736\pi$
$810$	24958.3	−	17860.3i	1.08265	−	0.774751i
$811$	24621.3			1.06605			0.533027	−	0.846098i	$-0.321054\pi$
$811$	24621.3			1.06605			0.533027	+	0.846098i	$0.321054\pi$
$812$	2920.21	+	2920.21i	0.126206	+	0.126206i
$813$	−637.200	−	408.570i	−0.0274878	−	0.0176250i
$814$		−	29365.6i		−	1.26445i
$815$	−41147.3	−	10061.8i	−1.76850	−	0.432454i
$816$	−7587.02	−	34703.5i	−0.325489	−	1.48881i
$817$	−3364.54	+	3364.54i	−0.144076	+	0.144076i
$818$	22671.6	−	22671.6i	0.969063	−	0.969063i
$819$	594.890	+	1295.50i	0.0253811	+	0.0552729i
$820$	−5243.58	+	3183.01i	−0.223309	+	0.135556i
$821$			14268.3i			0.606538i	0.952905	+	0.303269i	$0.0980781\pi$
$821$			14268.3i			0.606538i	−0.952905	+	0.303269i	$0.901922\pi$
$822$	16314.0	−	25443.1i	0.692234	−	1.07960i
$823$	13764.1	+	13764.1i	0.582972	+	0.582972i	0.935719	−	0.352747i	$-0.114752\pi$
$823$	13764.1	+	13764.1i	0.582972	+	0.582972i	−0.352747	+	0.935719i	$0.614752\pi$
$824$	7510.81			0.317538
$825$	11036.2	+	19231.2i	0.465737	+	0.811571i
$826$	20986.0			0.884015
$827$	27442.5	+	27442.5i	1.15389	+	1.15389i	0.985765	+	0.168128i	$0.0537721\pi$
$827$	27442.5	+	27442.5i	1.15389	+	1.15389i	0.168128	+	0.985765i	$0.446228\pi$
$828$	4214.50	−	11371.6i	0.176889	−	0.477282i
$829$		−	12176.9i		−	0.510159i	−0.966920	−	0.255080i	$-0.917898\pi$
$829$		−	12176.9i		−	0.510159i	0.966920	−	0.255080i	$-0.0821016\pi$
$830$	11094.9	−	6734.93i	0.463987	−	0.281654i
$831$	7714.23	−	1686.52i	0.322026	−	0.0704027i
$832$	−728.995	+	728.995i	−0.0303766	+	0.0303766i
$833$	−10783.2	+	10783.2i	−0.448519	+	0.448519i
$834$	−47756.5	+	10440.7i	−1.98282	+	0.433492i
$835$	−2143.22	−	524.085i	−0.0888255	−	0.0217206i
$836$			4023.21i			0.166442i
$837$	−1823.80	+	12971.5i	−0.0753165	+	0.535675i
$838$	31790.7	+	31790.7i	1.31049	+	1.31049i
$839$	−13942.3			−0.573710			−0.286855	−	0.957974i	$-0.592610\pi$
$839$	−13942.3			−0.573710			−0.286855	+	0.957974i	$0.592610\pi$
$840$	129.614	−	5270.46i	0.00532394	−	0.216486i
$841$	−21838.3			−0.895417
$842$	−28951.3	−	28951.3i	−1.18495	−	1.18495i
$843$	−5666.33	+	8837.14i	−0.231505	+	0.361053i
$844$		−	67.5849i		−	0.00275636i
$845$	−12653.7	−	20845.2i	−0.515149	−	0.848637i
$846$	5002.35	−	2297.06i	0.203291	−	0.0933505i
$847$	1549.96	−	1549.96i	0.0628776	−	0.0628776i
$848$	25929.6	−	25929.6i	1.05003	−	1.05003i
$849$	3767.30	+	17231.8i	0.152289	+	0.696579i
$850$	−37935.1	−	19732.6i	−1.53078	−	0.796261i
$851$		−	16606.6i		−	0.668937i
$852$	19834.7	+	12717.9i	0.797567	+	0.511396i
$853$	−32654.2	−	32654.2i	−1.31074	−	1.31074i	−0.920871	−	0.389866i	$-0.872521\pi$
$853$	−32654.2	−	32654.2i	−1.31074	−	1.31074i	−0.389866	−	0.920871i	$-0.627479\pi$
$854$	−99.6646			−0.00399350
$855$	−3226.03	+	4769.03i	−0.129039	+	0.190757i
$856$	−11348.8			−0.453147
$857$	10358.9	+	10358.9i	0.412898	+	0.412898i	0.882747	−	0.469849i	$-0.155692\pi$
$857$	10358.9	+	10358.9i	0.412898	+	0.412898i	−0.469849	+	0.882747i	$0.655692\pi$
$858$	2243.28	+	1438.38i	0.0892590	+	0.0572325i
$859$			14100.5i			0.560072i	0.959990	+	0.280036i	$0.0903464\pi$
$859$			14100.5i			0.560072i	−0.959990	+	0.280036i	$0.909654\pi$
$860$	−4093.57	+	16740.5i	−0.162313	+	0.663773i
$861$	−1304.10	−	5965.05i	−0.0516187	−	0.236107i
$862$	−20245.0	+	20245.0i	−0.799941	+	0.799941i
$863$	16830.6	−	16830.6i	0.663872	−	0.663872i	−0.292419	−	0.956290i	$-0.594460\pi$
$863$	16830.6	−	16830.6i	0.663872	−	0.663872i	0.956290	+	0.292419i	$0.0944601\pi$
$864$	−25603.9	+	19291.6i	−1.00818	+	0.759621i
$865$	3311.09	−	13540.6i	0.130151	−	0.532246i
$866$		−	24928.3i		−	0.978174i
$867$	9368.17	−	14610.5i	0.366966	−	0.572316i
$868$	−5398.60	−	5398.60i	−0.211106	−	0.211106i
$869$	20073.5			0.783597
$870$	7617.73	+	8001.86i	0.296857	+	0.311826i
$871$	2431.71			0.0945984
$872$	6131.84	+	6131.84i	0.238131	+	0.238131i
$873$	−15471.3	−	5733.92i	−0.599797	−	0.222295i
$874$			5220.88i			0.202058i
$875$	−13911.0	−	12188.0i	−0.537462	−	0.470892i
$876$	−15439.8	+	3375.51i	−0.595504	+	0.130192i
$877$	9832.57	−	9832.57i	0.378589	−	0.378589i	−0.492004	−	0.870593i	$-0.663736\pi$
$877$	9832.57	−	9832.57i	0.378589	−	0.378589i	0.870593	+	0.492004i	$0.163736\pi$
$878$	−22919.9	+	22919.9i	−0.880990	+	0.880990i
$879$	18185.1	−	3975.70i	0.697802	−	0.152556i
$880$	−14903.8	−	24552.0i	−0.570917	−	0.940508i
$881$			41729.4i			1.59580i	0.602789	+	0.797900i	$0.294056\pi$
$881$			41729.4i			1.59580i	−0.602789	+	0.797900i	$0.705944\pi$
$882$	16002.6	+	5930.84i	0.610925	+	0.226419i
$883$	−11757.3	−	11757.3i	−0.448090	−	0.448090i	0.446629	−	0.894719i	$-0.352624\pi$
$883$	−11757.3	−	11757.3i	−0.448090	−	0.448090i	−0.894719	+	0.446629i	$0.852624\pi$
$884$	−2239.51			−0.0852070
$885$	24458.2	+	601.490i	0.928987	+	0.0228462i
$886$	34437.1			1.30580
$887$	−24303.5	−	24303.5i	−0.919989	−	0.919989i	0.0770388	−	0.997028i	$-0.475453\pi$
$887$	−24303.5	−	24303.5i	−0.919989	−	0.919989i	−0.997028	+	0.0770388i	$0.975453\pi$
$888$	−4393.67	+	6852.32i	−0.166038	+	0.258951i
$889$			8227.16i			0.310383i
$890$	52017.9	+	12720.0i	1.95915	+	0.479074i
$891$	18875.3	+	16218.8i	0.709702	+	0.609820i
$892$	−5137.84	+	5137.84i	−0.192856	+	0.192856i
$893$	−730.214	+	730.214i	−0.0273636	+	0.0273636i
$894$	14920.4	+	68246.6i	0.558178	+	2.55314i
$895$	−24016.2	+	14578.6i	−0.896953	+	0.544478i
$896$			11314.9i			0.421881i
$897$	1268.60	+	813.418i	0.0472210	+	0.0302779i
$898$	948.871	+	948.871i	0.0352609	+	0.0352609i
$899$	−4715.44			−0.174937
$900$	−1025.08	+	20828.6i	−0.0379659	+	0.771430i
$901$	44269.1			1.63687
$902$	−8070.84	−	8070.84i	−0.297927	−	0.297927i
$903$	−14441.1	−	9259.55i	−0.532191	−	0.341239i
$904$		−	3696.50i		−	0.136000i
$905$	2578.52	−	1565.24i	0.0947105	−	0.0574922i
$906$	11229.3	+	51363.6i	0.411776	+	1.88349i
$907$	1017.75	−	1017.75i	0.0372589	−	0.0372589i	−0.688232	−	0.725491i	$-0.741613\pi$
$907$	1017.75	−	1017.75i	0.0372589	−	0.0372589i	0.725491	+	0.688232i	$0.241613\pi$
$908$	21262.7	−	21262.7i	0.777124	−	0.777124i
$909$	40787.3	−	18729.4i	1.48826	−	0.683404i
$910$	−2159.17	−	527.985i	−0.0786548	−	0.0192336i
$911$		−	33165.2i		−	1.20616i	−0.797681	−	0.603080i	$-0.793940\pi$
$911$		−	33165.2i		−	1.20616i	0.797681	−	0.603080i	$-0.206060\pi$
$912$	4025.67	−	6278.38i	0.146166	−	0.227958i
$913$	7441.88	+	7441.88i	0.269759	+	0.269759i
$914$	−8056.00			−0.291541
$915$	−116.154	−	2.85654i	−0.00419666	−	0.000103207i
$916$	10382.9			0.374521
$917$	13094.2	+	13094.2i	0.471546	+	0.471546i
$918$	−47525.4	−	6682.13i	−1.70869	−	0.240243i
$919$			2162.18i			0.0776103i	0.999247	+	0.0388051i	$0.0123552\pi$
$919$			2162.18i			0.0776103i	−0.999247	+	0.0388051i	$0.987645\pi$
$920$	−2891.96	−	4764.10i	−0.103636	−	0.170726i
$921$	−22684.9	+	4959.46i	−0.811609	+	0.177437i
$922$	35433.7	−	35433.7i	1.26567	−	1.26567i
$923$	−2070.30	+	2070.30i	−0.0738297	+	0.0738297i
$924$	−14170.2	+	3097.95i	−0.504508	+	0.110298i
$925$	8595.52	+	27231.6i	0.305534	+	0.967966i
$926$			6589.59i			0.233852i
$927$	10277.2	−	27729.9i	0.364129	−	0.982493i
$928$	−8160.29	−	8160.29i	−0.288658	−	0.288658i
$929$	17695.1			0.624929			0.312464	−	0.949930i	$-0.398846\pi$
$929$	17695.1			0.624929			0.312464	+	0.949930i	$0.398846\pi$
$930$	−14082.9	−	14793.1i	−0.496556	−	0.521595i
$931$	−3201.72			−0.112709
$932$	−13017.4	−	13017.4i	−0.457508	−	0.457508i
$933$	20211.3	−	31521.3i	0.709204	−	1.10607i
$934$			43676.6i			1.53013i
$935$	8236.07	−	33681.0i	0.288073	−	1.17806i
$936$	−308.248	−	671.277i	−0.0107643	−	0.0234417i
$937$	−30208.0	+	30208.0i	−1.05320	+	1.05320i	−0.0547017	+	0.998503i	$0.517421\pi$
$937$	−30208.0	+	30208.0i	−1.05320	+	1.05320i	−0.998503	+	0.0547017i	$0.982579\pi$
$938$	−21477.1	+	21477.1i	−0.747602	+	0.747602i
$939$	−3184.96	−	14568.2i	−0.110689	−	0.506300i
$940$	−888.437	+	3633.22i	−0.0308272	+	0.126067i
$941$		−	1499.59i		−	0.0519503i	−0.999663	−	0.0259752i	$-0.991731\pi$
$941$		−	1499.59i		−	0.0519503i	0.999663	−	0.0259752i	$-0.00826908\pi$
$942$	−42172.4	−	27040.8i	−1.45865	−	0.935282i
$943$	−4564.14	−	4564.14i	−0.157613	−	0.157613i
$944$	−31691.2			−1.09265
$945$	−19281.2	−	7690.22i	−0.663722	−	0.264722i
$946$	−32067.5			−1.10212
$947$	−13763.8	−	13763.8i	−0.472294	−	0.472294i	0.430362	−	0.902656i	$-0.358386\pi$
$947$	−13763.8	−	13763.8i	−0.472294	−	0.472294i	−0.902656	+	0.430362i	$0.858386\pi$
$948$	15892.8	+	10190.4i	0.544488	+	0.349123i
$949$		−	1963.89i		−	0.0671767i
$950$	−2702.32	−	8561.25i	−0.0922892	−	0.292383i
$951$	−1081.72	−	4947.87i	−0.0368847	−	0.168713i
$952$	−5829.59	+	5829.59i	−0.198464	+	0.198464i
$953$	−14570.7	+	14570.7i	−0.495268	+	0.495268i	−0.909961	−	0.414693i	$-0.863889\pi$
$953$	−14570.7	+	14570.7i	−0.495268	+	0.495268i	0.414693	+	0.909961i	$0.363889\pi$
$954$	−20674.1	−	45022.4i	−0.701625	−	1.52794i
$955$	−14041.1	−	23130.8i	−0.475768	−	0.783763i
$956$			1613.47i			0.0545851i
$957$	−4835.57	+	7541.49i	−0.163335	+	0.254735i
$958$	30404.7	+	30404.7i	1.02540	+	1.02540i
$959$	−20442.8			−0.688355
$960$	369.077	−	15007.7i	0.0124082	−	0.504552i
$961$	−21073.6			−0.707380
$962$	2426.75	+	2426.75i	0.0813322	+	0.0813322i
$963$	−15528.8	+	41899.7i	−0.519635	+	1.40208i
$964$		−	37082.4i		−	1.23895i
$965$	30184.4	+	7381.04i	1.00691	+	0.246222i
$966$	−18388.6	+	4020.18i	−0.612466	+	0.133900i
$967$	28409.1	−	28409.1i	0.944752	−	0.944752i	−0.0538000	−	0.998552i	$-0.517133\pi$
$967$	28409.1	−	28409.1i	0.944752	−	0.944752i	0.998552	+	0.0538000i	$0.0171333\pi$
$968$	−803.127	+	803.127i	−0.0266668	+	0.0266668i
$969$	8795.95	−	1923.01i	0.291606	−	0.0637522i
$970$	21992.1	−	13349.9i	0.727963	−	0.441896i
$971$		−	18059.4i		−	0.596864i	−0.954431	−	0.298432i	$-0.903536\pi$
$971$		−	18059.4i		−	0.596864i	0.954431	−	0.298432i	$-0.0964637\pi$
$972$	6710.61	+	22423.1i	0.221443	+	0.739938i
$973$	23379.9	+	23379.9i	0.770323	+	0.770323i
$974$	32307.7			1.06284
$975$	−2501.28	−	677.227i	−0.0821590	−	0.0222447i
$976$	150.505			0.00493600
$977$	31166.3	+	31166.3i	1.02057	+	1.02057i	0.999784	+	0.0207872i	$0.00661725\pi$
$977$	31166.3	+	31166.3i	1.02057	+	1.02057i	0.0207872	+	0.999784i	$0.493383\pi$
$978$	40013.6	−	62404.7i	1.30828	−	2.04037i
$979$			43422.9i			1.41757i
$980$	−9912.89	+	6017.43i	−0.323118	+	0.196143i
$981$	31029.1	−	14248.5i	1.00987	−	0.463729i
$982$	23907.2	−	23907.2i	0.776893	−	0.776893i
$983$	−13839.4	+	13839.4i	−0.449042	+	0.449042i	−0.895036	−	0.445994i	$-0.852850\pi$
$983$	−13839.4	+	13839.4i	−0.449042	+	0.449042i	0.445994	+	0.895036i	$0.352850\pi$
$984$	675.734	+	3090.85i	0.0218919	+	0.100135i
$985$	12787.8	+	3127.02i	0.413659	+	0.101153i
$986$		−	17276.6i		−	0.558012i
$987$	−3134.18	−	2009.62i	−0.101076	−	0.0648095i
$988$	−332.474	−	332.474i	−0.0107059	−	0.0107059i
$989$	−18134.5			−0.583056
$990$	−38100.5	+	7353.16i	−1.22314	+	0.236059i
$991$	17820.9			0.571242			0.285621	−	0.958343i	$-0.407800\pi$
$991$	17820.9			0.571242			0.285621	+	0.958343i	$0.407800\pi$
$992$	15085.9	+	15085.9i	0.482842	+	0.482842i
$993$	35984.5	+	23073.1i	1.14998	+	0.737363i
$994$		−	36570.2i		−	1.16694i
$995$	8937.56	+	14723.4i	0.284764	+	0.469109i
$996$	2114.07	+	9669.89i	0.0672559	+	0.307633i
$997$	−36985.0	+	36985.0i	−1.17485	+	1.17485i	−0.193814	+	0.981038i	$0.562086\pi$
$997$	−36985.0	+	36985.0i	−1.17485	+	1.17485i	−0.981038	+	0.193814i	$0.937914\pi$
$998$	−20433.7	+	20433.7i	−0.648114	+	0.648114i
$999$	19286.8	+	25597.6i	0.610819	+	0.810684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.4.e.a.8.1	yes	8
3.2	odd	2	inner	15.4.e.a.8.4	yes	8
4.3	odd	2		240.4.v.c.113.4		8
5.2	odd	4	inner	15.4.e.a.2.4	yes	8
5.3	odd	4		75.4.e.c.32.1		8
5.4	even	2		75.4.e.c.68.4		8
12.11	even	2		240.4.v.c.113.3		8
15.2	even	4	inner	15.4.e.a.2.1	✓	8
15.8	even	4		75.4.e.c.32.4		8
15.14	odd	2		75.4.e.c.68.1		8
20.7	even	4		240.4.v.c.17.3		8
60.47	odd	4		240.4.v.c.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.1	✓	8	15.2	even	4	inner
15.4.e.a.2.4	yes	8	5.2	odd	4	inner
15.4.e.a.8.1	yes	8	1.1	even	1	trivial
15.4.e.a.8.4	yes	8	3.2	odd	2	inner
75.4.e.c.32.1		8	5.3	odd	4
75.4.e.c.32.4		8	15.8	even	4
75.4.e.c.68.1		8	15.14	odd	2
75.4.e.c.68.4		8	5.4	even	2
240.4.v.c.17.3		8	20.7	even	4
240.4.v.c.17.4		8	60.47	odd	4
240.4.v.c.113.3		8	12.11	even	2
240.4.v.c.113.4		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +O(q^{10})\)	\(q+(-2.66260 - 2.66260i) q^{2} +(-4.37420 - 2.80471i) q^{3} +6.17891i q^{4} +(9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 - 9.35782i) q^{7} +(-4.84884 + 4.84884i) q^{8} +(11.2672 + 24.5367i) q^{9} +(-40.8945 - 10.0000i) q^{10} -34.1375i q^{11} +(17.3301 - 27.0278i) q^{12} +(2.82109 + 2.82109i) q^{13} -49.8323 q^{14} +(-58.0772 - 1.42827i) q^{15} +75.2524 q^{16} +(64.2384 + 64.2384i) q^{17} +(35.3316 - 95.3316i) q^{18} +19.0735i q^{19} +(35.8474 + 59.0536i) q^{20} +(-67.1789 + 14.6869i) q^{21} +(-90.8945 + 90.8945i) q^{22} +(-51.4018 + 51.4018i) q^{23} +(34.8094 - 7.61018i) q^{24} +(57.6836 - 110.895i) q^{25} -15.0229i q^{26} +(19.5337 - 138.930i) q^{27} +(57.8211 + 57.8211i) q^{28} +50.5042 q^{29} +(150.834 + 158.439i) q^{30} -93.3673 q^{31} +(-161.576 - 161.576i) q^{32} +(-95.7458 + 149.324i) q^{33} -342.083i q^{34} +(35.1454 - 143.725i) q^{35} +(-151.610 + 69.6188i) q^{36} +(-161.537 + 161.537i) q^{37} +(50.7850 - 50.7850i) q^{38} +(-4.42765 - 20.2524i) q^{39} +(-18.2109 + 74.4727i) q^{40} +88.7935i q^{41} +(217.976 + 139.765i) q^{42} +(176.399 + 176.399i) q^{43} +210.932 q^{44} +(250.035 + 169.137i) q^{45} +273.725 q^{46} +(38.2843 + 38.2843i) q^{47} +(-329.169 - 211.061i) q^{48} +167.863i q^{49} +(-448.857 + 141.680i) q^{50} +(-100.821 - 461.162i) q^{51} +(-17.4313 + 17.4313i) q^{52} +(344.569 - 344.569i) q^{53} +(-421.925 + 317.904i) q^{54} +(-198.051 - 326.262i) q^{55} +90.7492i q^{56} +(53.4956 - 83.4310i) q^{57} +(-134.473 - 134.473i) q^{58} -421.133 q^{59} +(8.82514 - 358.854i) q^{60} +2.00000 q^{61} +(248.600 + 248.600i) q^{62} +(335.046 + 124.174i) q^{63} +258.409i q^{64} +(43.3287 + 10.5952i) q^{65} +(652.524 - 142.657i) q^{66} +(430.987 - 430.987i) q^{67} +(-396.923 + 396.923i) q^{68} +(369.009 - 80.6742i) q^{69} +(-476.262 + 289.105i) q^{70} +733.866i q^{71} +(-173.607 - 64.3420i) q^{72} +(-348.073 - 348.073i) q^{73} +860.216 q^{74} +(-563.347 + 323.288i) q^{75} -117.853 q^{76} +(-319.452 - 319.452i) q^{77} +(-42.1349 + 65.7131i) q^{78} +588.019i q^{79} +(719.209 - 436.582i) q^{80} +(-475.102 + 552.919i) q^{81} +(236.422 - 236.422i) q^{82} +(-217.997 + 217.997i) q^{83} +(-90.7492 - 415.092i) q^{84} +(986.629 + 241.262i) q^{85} -939.362i q^{86} +(-220.915 - 141.650i) q^{87} +(165.527 + 165.527i) q^{88} -1272.00 q^{89} +(-215.399 - 1116.09i) q^{90} +52.7985 q^{91} +(-317.607 - 317.607i) q^{92} +(408.407 + 261.868i) q^{93} -203.872i q^{94} +(110.656 + 182.291i) q^{95} +(253.591 + 1159.94i) q^{96} +(-432.111 + 432.111i) q^{97} +(446.951 - 446.951i) q^{98} +(837.622 - 384.633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more